Fill a bowl with ice water and set aside.
Bring a large pot of water to a boil. Salt the water.
Shell peas: remove peas from their pod and add peas to boiling water. Quickly blanch the peas in the boiling water for about one minute. Taste a pea; it should lose its raw taste but remain crisp. For frozen peas, boil just until the peas are no longer frozen, about 3 minutes.
Remove peas from boiling water and place in an ice bath to cool. Once the peas feel cool, remove them from ice bath and drain.
Cut snap peas into thin, long strips.
Place peas, snap peas, mint, oil, salt, and pepper in a bowl and gently toss to combine.
Top with parmesan and burrata.