Combine flour, 8 tablespoons butter, yogurt, and salt in mixing bowl.
Work the mixture until it comes together as a dough. Place the dough between 2 sheets of parchment paper and roll it out to a thickness of ¼ inch.
Chill the dough for 30 minutes.
Preheat oven to 450° and line 2 baking sheets with parchment paper. Melt the remaining 2 tablespoons butter.
Cut the dough into 2-inch rounds using a cookie cutter and place them on the baking sheets. Brush each cracker with melted butter and sprinkle with sea salt.
Slide crackers into oven and bake until crisp, about 12 minutes. Remove from oven and cool completely before serving