In a small Dutch oven, melt the 2 tablespoons butter over medium heat. Add the apples, then stir in 1/2 cup sugar, the lemon juice and cinnamon. Cover and simmer until the apples are nearly tender, about 8 minutes. Stir in 1 tablespoon flour and remove from the heat.
In a medium bowl, combine the remaining 1 cup flour, 2 tablespoons sugar, the baking powder, baking soda and salt. Add the 3 tablespoons chilled butter, working it in with your fingertips until crumbly. Add the milk and stir to combine.
Return the Dutch oven to medium-low heat and spoon the batter onto the hot fruit to almost cover the surface. Cover and simmer until the batter is cooked through, about 20 minutes.