Preheat oven to 200 C / 400 F. Line a large baking tray with baking paper.
To make the beef filling, combine together minced meat, onion, carrot, breadcrumbs, garlic, paprika, cayenne pepper, tomato sauce (ketchup) and basil leaves in a large bowl. Season with salt and pepper. Divide the mixture into 5 equal portions. Set aside.
Lay one tortilla on a flat surface. Place ⅕th of the meat mixture along one side of the tortilla, shaping mince into a long sausage shape.
Roll up tortilla to enclose filling, finishing seam side down. Cut into 5 pieces.
Repeat with the remaining meat mixture and tortillas.
Place rolls seam side down on the baking tray.
Brush with egg.
Sprinkle with sesame seeds.
Bake for 20-25 minutes or until the tortillas are golden and cooked through.