In a 12-inch skillet, melt 2 tablespoons butter over medium-high heat. Add half the apples; cook, stirring, 5 minutes, until tender. Gently stir into sugar mixture. Repeat process with remaining 2 tablespoons butter and apples. Transfer filling to a 13" x 9" baking dish; cover and keep warm.
In a large bowl, combine flour, 1 tablespoon sugar, baking powder and salt. With a pastry blender or 2 knives used scissor-fashion, cut in butter until mixture resembles coarse crumbs. Stir in Cheddar and buttermilk. Turn dough onto a work surface (dough will be crumbly). Knead until dough is smooth and holds together.
Uncover filling. Drop dough by walnut-size pieces over apple mixture to cover; sprinkle with remaining 1/4 cup sugar. Bake until filling is hot and bubbling and biscuits are golden, 35 to 40 minutes. Let stand 15 minutes before serving. Top with vanilla ice cream.