NEW YORK, March 1 — Every Francophile has eaten a croque-monsieur, the French rendition of a grilled cheese sandwich. You can get one in any cafe or buy one from a bakery, ready to heat and eat. It is, for all intents, a hot ham and cheese sandwich, the top spread with a layer of creamy béchamel sauce and grated cheese, then broiled until golden and bubbly.

You eat a croque-monsieur served on a little plate, at a little table or standing at the bar, with a knife and fork.

A croque-madame is exactly the same, with a fried egg on top. Why is it madame when it has an egg?

No one really knows.

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Some think it looks like a 19th-century chapeau, but evidently it wasn’t ever called madame until 1960. At any rate, “madame” sounds more elegant than “put an egg on it.”

Of course, some versions are better than others, but you are guaranteed a satisfying, hot, cheesy morsel, whatever the caliber.

The old-fashioned benchmark croque-monsieur plants the ham and cheese between two thin white bread slices; then it is béchamel-slathered and bronzed in the oven. It is fetchingly displayed and perfectly adequate.

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But in many Parisian cafes, a croque is an open-faced affair, built on a sturdy toasted raft of rustic hearth-baked whole-wheat pain au levain, the type of traditional, naturally fermented sourdough bread made famous in Paris by the artisan baker Lionel Poilâne.

(This kind of bread is now relatively commonplace in artisanal US bakeries and perhaps taken for granted, but not so long ago, dedicated Americans had to order imported frozen pain Poilâne from a woman in Chicago or try to make their own.)

To my mind, this full-flavoured bread makes a tastier croque.

I decided to make an open-faced version of croque-madame with crab meat, which I thought would be a novel, entertaining and somewhat retro “fancy” approach to an elegant lunch. I intended to push it in a slightly Creole direction, adding cayenne, tarragon and chives. I even imagined tiny cocktail versions, topped with quail eggs.

Ladies and gentlemen, there is nothing new under the sun.

The crab meat spread atop thin-sliced ham and slices of bread, ready to bake for a croque-madame recipe with a seafood twist, in New York, February 21, 2017. — Picture by Karsten Moran/The New York Times
The crab meat spread atop thin-sliced ham and slices of bread, ready to bake for a croque-madame recipe with a seafood twist, in New York, February 21, 2017. — Picture by Karsten Moran/The New York Times

It seems someone had previously fiddled with the concept and invented crab toasties — unbeknown to me, a well-known, all-American, homey snack made with mayonnaise-dabbed crab meat, cheddar cheese and English muffins. And types of crab toasties are evidently popular in the British Isles, as well, where they are found at home or in a pub. I have been either traveling in the wrong circles or living under a rock.

It is unclear, however, if there has ever been a sandwich called crab meat croque-madame à la Créole. All you need is a pound of fresh crab meat and an open mind.

Crab Croque-Madame

Yield: 6 servings

Total time: 40 minutes

Unsalted butter

6 slices rustic country bread, about ½ inch thick, or day-old white bread, sliced ¾ inch thick

2 tablespoons all-purpose flour

2 cups whole milk, heated

Salt and pepper

Pinch of grated nutmeg

¼ cup crème fraîche

1 pound cooked crab meat

1 teaspoon paprika

Pinch of cayenne

Pinch of smoked Spanish pimentón dulce or chipotle powder

½ teaspoon grated lemon zest

2 teaspoons Dijon mustard

2 tablespoons snipped chives, plus more for garnish

1 teaspoon chopped tarragon

6 thin slices ham or prosciutto cotto

4 ounces grated white cheddar or Gruyère cheese, about 1 ½ cups

6 small eggs

1 tablespoon chopped parsley, for garnish

1.  Place a large cast-iron skillet over medium-high heat. Lightly butter both sides of each bread slice. Add slices to pan and let sizzle until crisp and golden on each side, working in batches if necessary. Place browned slices in one layer on a baking sheet and set aside.

2.  Make the béchamel: Melt 2 tablespoons butter in a heavy saucepan over medium heat. Whisk in flour and let cook for 1 minute without coloring. Whisk in milk, then turn heat to low and continue cooking. Adjust heat to keep sauce at a bare simmer, whisking occasionally, for about 5 minutes, until smooth and medium-thick. Season with salt, pepper and nutmeg and stir in crème fraîche. Set aside and keep warm.

3.  Heat oven to 425 degrees. In a medium bowl, combine crab meat, paprika, cayenne, pimentón, lemon zest and mustard. Add ½ cup warm béchamel sauce, the chives and the tarragon and stir well to combine.

4.  Put one thin slice of ham on each slice of grilled bread. Mound crab mixture onto each toast, dividing evenly among the 6 slices.

5.  Spoon remaining béchamel sauce evenly over crab mixture and sprinkle with cheese. Place baking sheet on top shelf in oven and bake for 10 minutes, until bubbling and well browned.

6.  Meanwhile, cook eggs sunny side up in a small amount of melted butter. To serve, top each crab toast with an egg. Sprinkle with chives and parsley. — The New York Times