Preheat the oven to 400 degrees F.
For the filling: Combine the sugar, flour and cinnamon in a large bowl. Add the apples, pears and apple juice or water; mix well. Transfer the mixture to a 1 1/2-quart shallow casserole dish or an 11-by-7-inch baking dish; top with the butter pieces.
For the dumplings: Combine the flour, sugar, baking powder and salt in a medium bowl. Add the cheese; mix well. Add the milk and butter; mix just until the dry ingredients are moistened. Drop the dough into 8 or 9 mounds over fruit mixture.
Bake until the filling is bubbly and the dumplings are golden brown, 30 to 35 minutes. Transfer to a wire cooling rack; let stand at least 20 minutes before serving. Serve warm.