Prep the garlic:
Peel the garlic cloves and remove the green germ (if present) to avoid bitterness. Add garlic and salt to a food processor and pulse until finely minced, scraping down the sides as needed.

Emulsify the sauce:
With the food processor running, begin slowly streaming in the oil — just a few drops at first — alternating with small amounts of lemon juice. This slow process helps emulsify the mixture. Continue alternating oil and lemon juice slowly until all is incorporated. The sauce should become fluffy and white, like mayonnaise.

Adjust with water if needed:
If the sauce becomes too thick or the emulsion looks like it’s breaking, add 1–2 tablespoons of ice water while blending to help it smooth out and come back together.

Store and serve:
Once the sauce is thick and creamy, transfer to a sealed container. Refrigerate for up to 3–4 weeks. Serve with grilled meats, sandwiches, roasted vegetables, or use it as a spread or dip.