Heat the oil in a large lidded skillet over medium-high heat. Cook the beef, onion and pepper for 7 to 8 minutes, breaking up the meat and cooking it to 160°F.
Stir in garlic, cumin and paprika for 30 seconds. Add the tomatoes, salt and red pepper; simmer uncovered for 4 minutes until the sauce thickens slightly.
Reduce to medium-low heat and make four wells in the sauce. Crack an egg into each well, cover and cook for 6 to 8 minutes until the whites and yolks are set.
Warm the pita breads in a dry skillet or microwave while the eggs cook.
Divide the eggs and beef sauce among four shallow bowls and serve with the warm pita.