Combine flour, 2 tablespoons sugar, salt, and baking soda in a large mixing bowl. Cut in 1/2 cup butter with a pastry blender until mixture resembles coarse meal. Add 2 cups buttermilk, stirring until dry ingredients are moistened.
Divide dough into 8 equal portions. Roll each portion into a 6- inch circle on a lightly floured surface. Place an apple on each circle. Fill each apple center with 2 teaspoons sugar, 1 teaspoon butter, and 1/8 teaspoon cinnamon. Moisten edges of dough with water. Fold dough over apple; pinch edges together to seal. Wrap each dumpling in a 12-inch square of cheesecloth; tie securely.
Place dumplings in a large Dutch oven with boiling salted water to cover. Simmer 35 to 40 minutes. Remove dumplings; discard cheesecloth. Place each dumpling in an individual serving bowl; top each with 1 tablespoon butter. Serve dumplings hot with dip.