Finely chop sun-dried tomatoes in a food processor. Blend in the mayonnaise and mustard.
Transfer mixture to a small bowl, cover and refrigerate until ready to use.

Finely chop Andouille sausage in clean processor. Transfer to a large bowl, add beef, shallots, salt, pepper and crushed fennel seeds.
Stir mixture with a fork just until blended. Form into 6 1 inch thick patties.

In a medium high heat grill, place hamburger buns for about 2 minutes until golden, remove to a platter.
Brush onion slices with olive oil, salt and pepper and grill for about 7 minutes.
Grill hamburgers about 5 minutes per side for medium rare. Allow another minute per side for medium.
Sprinkle cheese over top of hamburger.

Spread mayonnaise mixture on both sides of bun.
Place hamburger, red roasted peppers and cooked red onion.

Cover with top of bun and serve hot.