In a blender or mixing bowl, combine the buckwheat flour and salt.
Gradually add the cold water while whisking continuously to avoid lumps.
Add the egg and whisk until you have a smooth batter. Let it rest for at least 30 minutes at room temperature or in the refrigerator.
For the savory mushroom and Gruyere filling:
In a skillet, heat the butter and olive oil over medium heat.
Add the chopped onion and sauté for 2-3 minutes, or until it becomes translucent.
Add the sliced mushrooms and garlic to the skillet. Sauté for about 5-6 minutes, or until the mushrooms release their moisture and start to brown. Season with salt and pepper to taste.
Remove the skillet from heat and set aside.
Assembly and Cooking:
Heat a non-stick skillet or crepe pan over medium-high heat. Lightly grease the pan with a small amount of butter or oil.
Pour a ladleful of the buckwheat galette batter into the center of the hot skillet. Quickly lift and tilt the pan to spread the batter evenly across the bottom, forming a thin galette.
Cook for about 2-3 minutes, or until the edges start to lift and the bottom is golden brown.
Flip the galette using a spatula and cook for an additional 1-2 minutes on the other side.
Spoon some of the sautéed mushroom and Gruyere filling onto one half of the galette.
Fold the other half of the galette over the filling, creating a half-moon shape.
Repeat the process with the remaining batter and filling.