In a food processor, combine garlic, anchovies (with oil), and ½ teaspoon kosher salt. Process until finely chopped.

Add egg yolk, lemon juice, and Dijon mustard. Blend for 30 seconds.

With the machine running, slowly drizzle in olive oil and avocado oil until emulsified.

While still running, add 1–2 tablespoon water to loosen the consistency as needed.

Season with salt, black pepper, and additional lemon juice to taste.

Stir in Parmesan just before serving.