Cook potatoes in a pot of boiling water until easily pierced with a fork, 11 to 14 minutes; drain. Halve potatoes. Meanwhile, simmer peas in a saucepan of water until tender, about 4 minutes; drain, reserving 1/4 cup cooking liquid. Crush peas with 1 tablespoon olive oil and 2 tablespoons reserved cooking liquid using a fork. Gradually stir in remaining 2 tablespoons cooking liquid until mixture is thick and chunky. Toss potatoes with pea mixture, mint, salt, and some pepper. Drizzle with additional tablespoon oil.
Try pairing this with poached chicken.