For the savory buckwheat crepes: In a large bowl, whisk together the buckwheat flour, all-purpose flour, and salt. Add the milk and the egg and whisk vigorously until the batter is smooth. Cover and refrigerate for at least 2 hours, or preferably overnight.
To make the savory buckwheat crepes, place a crepe pan or non-stick skillet over medium-high heat. Lightly spray the pan with cooking oil or use a piece of paper towel to rub a little butter in the pan. Pour in 1/3 cup (80 ml) of the buckwheat crepe batter in the pan and quickly swirl it to spread the batter over the surface of the pan to create an 8-inch (20 cm) crepe. Let the savory buckwheat crepe brown on one side until crisp around the edge, about 1 minute. Flip the crepe over and cook 1 minute more.
Transfer the cooked crepe to a large plate and repeat the steps above to make all the crepes, stacking them on top of each other as they are finished. At this point, the crepes can be covered and refrigerated for up to 3 days, or frozen in an airtight container or a heavy-duty freezer bag for up to 1 month.
Set one savory buckwheat crepe flat on a working surface. Sprinkle with 1/4 cup (1 oz / 28 g) of the grated cheese, then top with 1 slice of ham. Fold the crepe in two, then again to create a quarter circle shape. Transfer to the prepared baking sheet. Repeat to assemble all the savory buckwheat crepes. Bake for 5 to 7 minutes, until the edges of the crepes are crispy, and the cheese is melted.
While the crepes are baking, fry the eggs sunny side up in a very hot oiled skillet, seasoning each with flaky sea salt and freshly ground black pepper.
Serve two folded savory buckwheat crepes per person and top each serving with 1 fried egg. Garnish with minced chives, if desired, and serve immediately with a green salad.
Recipe Credit: Adapted from David Tanis, The New York Times.
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