Place the basil, lime juice, olive oil, Parmesan cheese, garlic, salt, and pepper in a strong blender or food processor. Pulse until fully combined. Set aside.
1 cup chopped fresh basil, ½ lime, ¼ cup olive oil, ¼ cup freshly grated Parmesan cheese, 3 cloves garlic, 1 teaspoon fine sea salt, 1 teaspoon ground black pepper