Drape a kitchen towel over a small saucepan, and set a small metal bowl over it. Mash garlic and salt together in bowl; whisk in yolks and 2 tsp. warm water. Add oil, 1 tsp. at a time, whisking constantly. Add extra virgin olive oil in a slow, steady stream, whisking constantly. (If mixture gets too stiff, add more water.) Stir in lemon juice and pepper to taste. Serve with shrimp, eggs, and vegetables.
Lime-Sriracha Aïoli: Omit lemon juice and black pepper. Prepare recipe as directed, stirring in 2 tsp. each fresh lime juice and Asian hot chili sauce (such as Sriracha) after whisking in extra virgin olive oil.
Saffron Aïoli: Omit lemon juice and black pepper. Stir together 2 tsp. warm water and 1/2 tsp. crumbled saffron threads. Prepare recipe as directed, substituting saffron mixture for plain warm water. Stir in a pinch of dried crushed red pepper before serving.