Mussels with White Wine

INGREDIENTS

• 2 tablespoons olive oil
• 1 garlic clove, finely grated
• 4 pounds mussels, debearded, scrubbed
• 1/2 cup white wine
• 2 garlic cloves, finely chopped
• 1 medium yellow onion, chopped
• 2 tablespoons tomato paste
• 2 teaspoons fresh thyme leaves
• 1 teaspoon (or more) fresh lemon juice
• Kosher salt, freshly ground pepper
• 1 large egg yolk
• Sliced country-style bread, toasted (for serving)
• 1/4 cup vegetable oil
• Kosher salt
• 1/4 cup extra-virgin olive oil