Heat oil. Sauté onion with salt, covered, until softened, 5 minutes.
Stir in Cajun seasoning and cayenne. Cook until fragrant, 1 minute.
Add beef. Cook, breaking up, until just pink, 3 minutes.
Stir in tomato purée, ketchup, and pepper. Simmer until thickened, 8 to 10 minutes.
Season to taste. Spoon onto hamburger buns and serve warm.