Bring a medium pot of water to a boil; add the peas and cook until just tender, about 5 minutes. Drain in a colander and rinse under cold water to cool.
With the motor running, add the garlic to the food processor through the shoot to finely chop. Add the peas, mayonnaise, lemon, olive oil, dill, cayenne, 1/4 teaspoon salt and a few grinds of pepper and process until smooth.
Transfer the aioli to a small bowl. Serve with assorted veggies for dipping.