In a food processor, pulse minced garlic, lemon juice, and yolks until well combined. Add salt and, with motor running, drizzle in 1 tbsp. cold water, followed by oil in a thin stream. (If it becomes too thick, add a few tablespoons of cold water to make a loose, creamy sauce and to keep it from separating.) Season to taste with salt.
Make ahead: Up to 2 days, chilled, with plastic wrap pressed against surface.