Place marshmallows and milk in a large microwave-safe bowl. Microwave, uncovered, on high for 30-90 seconds. Stir until smooth; set aside.
Finely chop the peaches; mash lightly with a fork or pulse in a food processor until finely chopped. Add to marshmallow mixture. Stir in extract. Fold in whipped topping; pour into crust. Refrigerate for 2 hours.