Toss leftover pesto with pasta, spread it on sandwiches, or serve it as a dip for crudites.
Bring a medium pot of water to a boil. Gently lower eggs into water. Turn off heat and cover; let eggs stand until whites are just set but yolks are still runny, about 6 minutes. Transfer to an ice-water bath and let cool completely.
Meanwhile, blanch fresh peas in a medium pot of salted boiling water until bright green and just tender, 3 to 4 minutes. Transfer to another ice-water bath and let cool completely. Drain. (If using frozen peas, skip this step.)
In a food processor, pulse peas, garlic, pine nuts, basil, and Parmesan until a paste forms. With machine running, slowly add oil, processing until combined. Season with salt and pepper.
Spread each piece of toast with 2 tablespoons pea pesto. Peel eggs and slice in half; divide among toasts. Season with salt and pepper, top with basil leaves, and serve.