Finely chop sun-dried tomatoes in food processor. Blend in mayonnaise and mustard. Transfer to small bowl and cover and chill. Can be made up to 1 day ahead.
Finely chop andouille sausage in processor. Transfer to large bowl. Add beef, shallots, salt, pepper and fennel seeds. Stir with fork just until blended. Form mixture into 6 patties.
Prepare barbecue on medium high heat. Grill hamburger buns until golden brown for 2min. Transfer to plate. Brush onion slices with oil. Sprinkle with salt & pepper. Grill until golden about 7min. per side. Grill until desired doneness. Sprinkle cheese over top of burgers.
Spread hamburger buns with sun-dried tomato mayonnaise. Top with red bell peppers. Top with onion slices. Then place hamburgers on and tops of buns.