Preheat the oven to 375 degrees . Grease an 8-by-12-inch baking dish and set aside. In a large skillet, heat 2 tablespoons butter over medium-high heat. Add the onion and cook, stirring, until softened but not browned, 3 to 5 minutes. Add the beef and cook, breaking it up with the back of a spoon, until no longer pink, about 5 minutes. Stir in the tomatoes and beef broth and season with salt and pepper. Lower the heat and cook, stirring occasionally, until most of the liquid has cooked off, about 20 minutes. Pour into the prepared baking dish and spread evenly.
Meanwhile, in a large bowl, combine the flour, baking powder and 1/2 teaspoon salt. Using your fingertips or a pastry blender, blend in the remaining 4 tablespoons butter and the cheese until the mixture resembles coarse crumbs. Pour in the milk and stir quickly with a fork to form a dry, shaggy dough. Gather the dough together and knead lightly in the bowl. Transfer to a floured work surface and roll or pat into a large, 1/2-inch-thick round. Using a 3-inch cookie cutter, cut out 8 biscuits. Gather the scraps of dough, form into a new round and cut out more biscuits. Continue until all the dough has been used.
Place the biscuits on top of the beef mixture as close together as possible and bake until lightly browned, about 35 minutes.