How to Make It
In a medium bowl, whisk the buckwheat flour with the eggs and half of the milk until lump-free. Add the remaining milk and whisk until smooth. Refrigerate the batter for 20 minutes.
Meanwhile, in a large nonstick skillet, heat the 1 tablespoon of oil. Add the shallots and cook over moderately high heat until soft, about 2 minutes. Add the mushrooms, season with salt and cook until tender, about 4 minutes. Add the garlic and cook 1 minute longer. Add the wine, scraping up any browned bits from the bottom of the skillet and cook until the liquid has evaporated, about 2 minutes.
Heat an 8-inch nonstick skillet and lightly brush with olive oil. Add 1/4 cup of the batter to the skillet and swirl to coat the pan. Cook over moderate heat until the edges begin to pull away from the pan, 30 seconds to 1 minute. Flip the crêpe and cook 30 seconds to 1 minute longer.
Sprinkle the crêpe with 1/4 cup of cheese followed by 1/4 cup of the mushrooms. Fold the bottom flaps of the crêpe to form a cone. Slide the crêpe onto a serving platter. Repeat with the remaining batter, brushing the pan with oil as needed.
Serve the crêpes immediately.