Preheat oven to 400°F. Position a rack in the upper third of the oven.
In a large saucepan, heat the olive oil over medium heat. Add the onion, chili powder and cumin and cook, stirring, until the onion is soft, about 5 minutes.
Stir in the tomato paste. Add the beef and cook, breaking up the meat, for 5 minutes; season with salt and pepper.
Add the beans and the tomatoes with their juice and bring to a boil. Lower the heat, partially cover and simmer, stirring occasionally, for 20 minutes. Transfer to an 8-by-11-inch baking dish.
In a large bowl, combine the potatoes and cheese. Scatter the potato mixture over the chili. Place the baking dish on a baking sheet and bake until the potatoes are cooked through and the chili is bubbling, about 35 minutes.