2) Coarsely chop the pepper and place it in the bowl of a food processor. Add the yolks, garlic, vinegar, chilli paste and salt to taste. Puree until the mixture is homogeneous. While the machine is running VERY slowly drizzle in the oil, until incorporated.
3) Check the aioli for texture and flavour. If it's too thick, add a few drops of water to thin it down, or on the flip side if it's too thin add more oil. The desired outcome is a fairly thin aioli. Check the flavour and add more salt or chilli paste, if desired. Refrigerate until ready to use.
For the mussels:
1) Generously coat a pan large enough to accommodate all the mussels with olive oil . Add the onions and bring to a medium-high heat, stirring frequently. Cook the onions until they are very soft and aromatic but have no colour.
2) Add the garlic, thyme and bay leaf and cook for another 2 to 3 mins. Stir to be sure the garlic doesn't burn. Add the mussels and stir to coat with the oil. Add the wine and cover the pot. Steam the mussels for 5 to 6 mins or until all the shells open. If some shells don't open, cook them for a little longer. Sometimes the freshest mussels are the most stubborn to open. Remove the mussels that don't open after longer cooking. When in doubt, throw out.
3) While the mussels are steaming, toast or grill the slices of bread.
4) Serve the mussels in individual bowls with lots of the juice from the bottom of the pan. Generously drizzle each bowl with the aioli. Garnish with toast. (You may want to have more toasted bread on hand to sop up the delicious liquid!)
*RAW EGG WARNING: Food Network Kitchens suggest caution in consuming raw and lightly-cooked eggs due to the slight risk of Salmonella or other food-borne illness. To reduce this risk, we recommend you use only fresh, properly-refrigerated, clean, grade A or AA eggs with intact shells, and avoid contact between the yolks or whites and the exterior of the shell.