Preheat the oven to 400˚F.
In a 10-inch oven-safe (preferably cast iron) skillet over moderate heat, melt the butter. Add the onion and sauté, stirring occasionally, until softened and translucent, about 5 minutes. Add the ground beef and cook, stirring occasionally, until browned, about 8 minutes. Add the salt and piment and stir to combine. Remove the skillet from the heat and set aside.
In a large bowl, combine the flour, baking powder and salt. Add the olive oil and milk and, using an electric hand mixer, beat until evenly combined. Add the eggs and beat again until smooth, about 1 minute. Pour the batter evenly over the beef in the skillet and transfer to the preheated oven. Bake until the batter is cooked through, and a knife inserted in the center comes away clean, about 30 minutes.
Arrange the sliced tomatoes in an even layer over the pie and top with the cheese. Return to the oven to bake for another 10 minutes, or until the cheese has melted and the tomatoes have softened. Serve immediately.
If you do not have an oven-safe skillet, you can transfer the sautéed beef and onion to a buttered pie plate, top with the batter, and bake as instructed.