Whisk buckwheat flour, 2 eggs, milk, water, and salt in a bowl until smooth with no lumps. Cover and rest at room temperature for 30 minutes to fully hydrate the flour.
1 cup buckwheat flour, 2 large egg, 1 cup milk, 0.25 cup water, 0.5 teaspoon salt
Warm a non-stick or crepe pan over medium heat and brush with melted butter to prevent sticking.
2 tablespoons butter
Pour ¼ cup of the batter into the center of the pan and immediately tilt in a circle to spread thin before the edges set (within 10 seconds). Cook the first side 1-2 minutes until edges lift and turn golden brown, then flip and cook the second side 30-60 seconds until light brown spots appear.
1 cup buckwheat flour
While the second side cooks, place 2 slices of ham and ¼ cup grated cheese on one half of the crepe. Meanwhile, crack one egg into a separate small pan on low heat and cook 3-5 minutes until the white sets but yolk remains soft. Slide cooked egg onto the ham and cheese, then fold the crepe in half and then in quarters.
8 slices ham, 1 cup Gruyère cheese, 4 large egg
Brush the pan with butter before each crepe and repeat cooking steps with remaining batter and fillings. Serve immediately while cheese is melted and eggs are warm. Garnish with fresh chives or parsley if desired.
2 tablespoons butter, fresh chives or parsley