1. In a large, non-corrosive pan, combine onion, 3/4 of the dill, bay leaves, red pepper flakes, pepper, wine and 3 cups water. Bring liquid to a boil, lower heat and simmer 10 minutes. Strain into a clean pan. (If desired, recipe may be done ahead to this point. Refrigerate broth and mussels)
2. Rinse (do not soak) mussels and remove wirelike beards if visible. Add salt and aquavit to the broth and bring to a boil. Add the mussels, cover and cook over medium-high heat until shells have opened, 3 to 5 minutes.
3. Remove pan from heat and discard mussels whose shells remain closed. Remove remaining mussels from their shells and discard shells.
4. Mix mayonnaise with most of remaining dill (reserving some for garnish) and, if desired, aquavit to taste. Place mayonnaise in a small bowl (or spread on toasted bread). Place bowl on a plate and surround with the mussels, each one (or, depending on size, a pair) speared with a toothpick; or cut each slice of toast into 6 pieces and top each with a mussel. Transfer to a platter, garnish with remaining dill and serve.