Galette Complete (Buckwheat Crêpe with Ham Cheese Egg)

For 2 servings, prepare 120 g buckwheat flour, 250 ml water, 4 eggs, 2 slices ham, 60 g Gruyere, 1 tablespoon butter, and 0.5 teaspoon salt. Whisk the flour with the water, 2 of the eggs, and the salt until no dry lumps remain. Rest the thin batter for 15 minutes so the buckwheat can hydrate and the texture can become smoother. Heat a wide skillet or crepe pan over medium heat and brush it with a very thin coating of butter. Pour in enough batter for one galette and tilt the pan immediately to spread it into a thin, even layer. Cook for 1 to 2 minutes, until the edges look dry and crisp and the center no longer appears wet. Place 1 slice of ham and about 30 g Gruyere in the center, then crack 1 egg over them. Keep the yolk intact and gently spread only the white so it sets quickly while the cheese melts underneath. Fold the four edges inward to create a square and lower the heat to medium-low. Cook for another 2 to 3 minutes. The galette is ready when the white is opaque and the yolk still jiggles softly. Repeat with the remaining batter, ham, cheese, and egg, serving each galette hot while its folded edges remain crisp.