Prepare the vegetables

1. Chop the onion and red pepper into small, bite-sized pieces. Cut the bottom stems from the Brussels Sprouts and remove any yellow leaves.
   
2. Using the shredding blade of a food processor, shred all the Brussels Sprouts to a coleslaw consistency, or finely chop by hand.
3. Heat the olive oil over medium low heat. Sauté the chopped onion for 5 minutes or until they begin to caramelize. Stir in the red pepper and cook for 2 more minutes.
4. Fold in all the shredded Brussels Sprouts and stir to coat with onion and pepper mixture. Cover and cook for 10 minutes, removing the lid often to stir and scrape the pan. Cook until Brussels Sprouts are bright green and tender, but not mushy or overcooked.
5. Remove from heat and pour directly into a large mixing bowl. Transfer the bowl to refrigerator to cool if serving chilled, otherwise, keep warm.
6. Pour aioli sauce over the vegetables and stir to coat. Add salt and pepper to taste if needed. Refrigerate before serving or serve immediately warm.

For the Aioli Sauce

1. In a large food processor, chop the fresh garlic. Add in roasted red peppers and blend until thoroughly chopped. Pulse in the egg yolks.
   
2. With the blade running, slowly pour in the olive oil, keeping a steady thin stream. Add lemon juice, salt, pepper, and paprika/cayenne, and pulse in fresh herbs at the end to roughly chop