Combine eggs, milk, and 2 tablespoons butter in a blender. Add buckwheat flour, all-purpose flour, and a pinch of salt; puree until smooth. Allow batter to rest in the refrigerator overnight.
Melt 3 tablespoons butter in a large skillet over medium-high heat. Stir in cremini mushrooms and cook until golden brown, about 10 minutes. Add tomatoes and spinach; cook and stir until wilted, 3 to 4 minutes. Set the filling aside.
Melt 1 teaspoon butter in a large skillet over medium heat. Pour about 1/4 cup batter per crepe (depending on the size of your pan) into the hot skillet and immediately tilt and swirl the pan to evenly distribute batter along the bottom. Cook until the center is set and edges begin to brown, 3 to 4 minutes. Sprinkle 1/4 of the filling in the middle of each crepe and sprinkle each with 3 tablespoons Gruyere cheese. Reserve remaining cheese. Fold the crepes in thirds over the filling, forming triangle shapes. Serve crepes with remaining Gruyere sprinkled on top.
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