Bring salted water to a rolling boil in a saucepan over high heat. Add peas. Cook until tender, about 5 minutes. Drain and set aside.
Reduce heat to medium and add butter to saucepan. Stir in radishes; cook, stirring often, until translucent, about 3 minutes.
Transfer radishes to a plate and return drained peas to pan. Mash peas lightly or until desired consistency with a potato masher. Stir in radishes and mint. Season with Parmesan cheese, salt, and black pepper to taste.