Mix the buckwheat flour with the salt, crack in the egg and gradually whisk in the water to get a smooth, thin batter. Cover and chill for at least 1 hour.
Heat a large (28 cm) flat frying pan over high heat and grease it thinly with butter.
Pour in a ladleful of batter, spread it quickly and thinly, and cook for 1-2 minutes until the underside is brownish and lacy and the edge comes away.
Turn it over, reduce the heat to medium, put the ham in the middle of the galette, sprinkle half the cheese around it and crack an egg into the centre.
Cover and cook for 2-3 minutes until the egg white has set, the yolk is still runny and the cheese has melted.
Fold the four edges of the galette towards the centre to make a square frame with the yolk showing. Season with pepper and serve at once. Make the second portion the same way.
Note: buckwheat is gluten-free, but shop-bought buckwheat flour may contain traces of gluten.
A Receptnaptár original recipe. Calories and protein are estimated.