In a large, heavy pot, heat the vegetable oil over medium-high heat. Add the onions, season with 1 teaspoon of salt and the cayenne, and cook, stirring, until they are wilted and golden, about 4 minutes. Season the meat with the remaining 1 teaspoon salt and add to the pot. Cook, stirring, until the beef is browned evenly on all sides, about 4 minutes. Add the tomato paste and cook, stirring, for 2 minutes. Add the tomatoes, beef broth, garlic, chili powder, cumin, oregano, red pepper flakes, and beans. Bring to a boil, then reduce the heat to medium-low and simmer, uncovered, stirring occasionally, until the beef is tender, about 2 hours. Skim off the fat that rises to the surface.
Preheat the fryer to 360 degrees F. Fry the potatoes in batches until golden brown, about 4 to 5 minutes. Remove and drain on paper towels. Season with salt and pepper. To serve, mound the potatoes over the bottom of each serving bowl. Ladle the chili over the potatoes. Sprinkle the cheese over the top. Garnish with parsley.