Step 1

Heat oil in large heavy pot over medium. Cook garlic, stirring often, until golden, about 2 minutes. Add parsley, mussels, wine, and red pepper flakes; stir to coat. Cover and cook, stirring halfway through, until mussels open, about 4 minutes. Uncover and transfer opened mussels to a large bowl with a slotted spoon. If any mussels are still closed, cover pot again and cook until opened, about 1 minute more. Transfer open mussels to bowl; discard any that remain closed. Chill mussels until ready to assemble. Strain cooking liquid; discard solids. Measure out 3 cups mussel stock; add water if short. Reserve pot.

Step 2

Heat oil in reserved pot over medium-low. Cook pepperoni, stirring often, until some fat has cooked out and oil is bright red, about 4 minutes. Add anchovy, tomato paste, and oregano. Cook, stirring often, until tomato paste darkens slightly, about 3 minutes. Add onion and garlic and cook, still stirring often, until onion is soft, about 4 minutes.

Step 3

Increase heat to medium-high and add wine. Cook, stirring, until wine is evaporated, about 3 minutes. Stir in rice and reserved mussel stock. Reduce heat to medium-low and cook, uncovered, stirring often, until stock is absorbed and rice is al dente, 20–25 minutes.

Step 4

Remove pot from heat and cover with lid; let stand 20 minutes. Uncover and stir in lemon juice and sugar. Chill pepperoni rice at least 30 minutes.Do Ahead: Rice can be made 3 days ahead. Let cool, then cover and chill.

Step 5

Place racks in upper and lower thirds of oven; preheat to 400°. Line 2 large rimmed baking sheets with lightly crumpled foil (to help keep mussel shells upright). Remove top shells from mussels (pry apart and twist at the hinge). Using a paring knife, loosen meat from bottom shells. Spoon 1 Tbsp. pepperoni rice over each mussel and shape into a mound. Divide mussels, stuffed side up, between baking sheets. Bake until warmed through, 5–8 minutes. Remove from oven; heat broiler.

Step 6

One baking sheet at a time, broil mussels on upper rack until tops are golden brown, 5–7 minutes (watch closely; broilers vary dramatically in power).

Step 7

Transfer mussels to a platter and drizzle with aioli. Serve with lemon wedges for squeezing over.