Instead of flipping the eggs, baste them with hot olive oil until set. Slideshow: Brunch Dishes
In a medium bowl, whisk the buckwheat flour with 2 of the eggs and half of the milk until lump-free. Add the remaining milk and whisk until smooth. Refrigerate the batter for 20 minutes.
Line a plate with wax paper. 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. Transfer the crêpe to the prepared plate and repeat with the remaining batter.
Wipe out the skillet and add 2 tablespoons of olive oil. Add an egg and fry until the edges begin to crisp, about 1 minute. Tilt the pan and spoon hot oil over the top of the egg until the top is set. Sprinkle the egg with flaky salt. Transfer a crêpe to a plate and set the egg on top. Cook the remaining eggs, adding more oil as necessary, and serve with the crêpes.