Separate one whole egg and reserve the yolk, add 1 teaspoon of Dijon mustard and the juice of one half of a medium lemon to the yolk. Whisk with a fork to combine and then transfer to an immersion blender container or a blender. Add grated garlic and mix on low speed.
Combine 1/4 cup olive oil and 3 tablespoons of vegetable oil in a beaked container, and while the blender is running, slowly pour in the combined oils. Mix on high until you get a light yellow thick mixture, the consistency of mayonnaise.
Place in serving containers and refrigerate until ready to use.
