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, heat the 1 tablespoon of olive oil in a large nonstick skillet. Add the garlic and cook over moderately high heat until fragrant, about 1 minute. Add the arugula and sauté until wilted, about 2 minutes. Season with salt.
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 1/4 cup of cheese over the crêpe followed by 2 tablespoons of arugula. Fold the crêpe in half. Slide the crêpe onto a serving platter. Repeat with the remaining batter and filling and serve.
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