- 1 large egg yolk
- 1 garlic clove, finely grated
- 1 teaspoon (or more) fresh lemon juice
- 1/4 cup vegetable oil
- 1/4 cup extra-virgin olive oil
- Kosher salt
- 2 tablespoons olive oil
- 1 medium yellow onion, chopped
- Kosher salt, freshly ground pepper
- 2 garlic cloves, finely chopped
- 2 tablespoons tomato paste
- 1/2 cup white wine
- 4 pounds mussels, debearded, scrubbed
- 2 teaspoons fresh thyme leaves
- Sliced country-style bread, toasted (for serving)
- Whisk egg yolk, garlic, and lemon juice in a medium bowl. Whisking constantly, drizzle in vegetable oil, then olive oil in a slow, steady stream; whisk until aioli is emulsified. Season with salt and more lemon juice, if desired. Cover; chill.
- DO AHEAD: Aioli can be made 1 day ahead. Keep chilled.
- Heat oil in a large heavy pot over medium-high heat. Add onion, season with salt and pepper, and cook, stirring often, until softened, about 5 minutes. Add garlic and cook, stirring often, until fragrant, about 1 minute. Add tomato paste and cook, stirring, until it begins to darken, about 2 minutes. Add wine and bring to a boil. Reduce heat and simmer until liquid is slightly reduced, about 1 minute.
- Add mussels and 1/2 cup water to pot, cover, and reduce heat to medium. Cook, stirring occasionally, until mussels open (discard any that do not open), 10-12 minutes.
- Ladle mussels and broth into shallow bowls and top with thyme; serve with bread and lemon aioli.