These savory biscuits are perfect for a breakfast or brunch gathering.
Heat oven to 400 degrees. Cut potatoes lengthwise; reserve 1/2 of 1 potato. Place remaining 1 1/2 potatoes in oven on center rack. Bake until fork-tender, about 30 minutes. Remove, and set aside. Increase oven temperature to 425 degrees. Once potatoes are cool, use paring knife to coax skins from flesh; discard skins. Pass potatoes through potato ricer into bowl to yield about 1 cup; set aside.
In bowl, mix together flour, salt, baking powder, and sugar. Using pastry cutter, cut in 8 tablespoons butter until it is size of peas. Add grated cheese and half of thyme leaves. In another bowl, mix reserved riced potatoes and milk; add to flour mixture. Mix just until moistened; turn onto lightly floured work surface.
Melt remaining 2 tablespoons butter. Flatten dough into 3/4-inch-thick disk. With 2-inch round cutter, cut out biscuits; place on ungreased baking sheet. Cut reserved raw potato into 18 thin slices with skins on. Lay 1 slice of potato on each biscuit, and brush with butter; sprinkle with remaining thyme leaves. Bake biscuits until golden brown, about 20 minutes. Cool slightly on a wire rack, and serve warm.
Swiss cheese may be substituted for the Gruyere cheese.