Peel the garlic cloves and remove any green sprouts. Add the garlic to a food processor or high-speed blender.
Add the lemon juice, aquafaba, Dijon mustard, and kosher salt. Blend for about 1 minute until the garlic is finely pureed.
With the blender running on low speed, slowly drizzle in the oil in a thin, steady stream until the dressing becomes thick, creamy, and smooth.
Taste and adjust with additional lemon juice or salt if needed. For a milder flavor, blend in the optional Greek yogurt.
Transfer the dressing to an airtight glass jar and refrigerate for at least 30 minutes before serving.
Stir or shake well before serving, then drizzle over salads, grain bowls, roasted vegetables, grilled meats, wraps, or use as a dipping sauce.