Add asparagus to a large pot of well-salted water and cook until just tender, about 4 minutes. Transfer (using a slotted spoon) to a large heatproof bowl. Add peas to boiling water and cook for 2 minutes. Transfer to bowl with asparagus and add linguine to water. Cook until al dente.
While linguine is cooking, add basil, mint, olive oil, salt, pepper, and ½ cup feta to the bowl of a food processor and pulse until all is pureed and combined. Add mixture to bowl with asparagus and peas.
When pasta is done cooking, reserve ½ cup water before draining. Stir this water into the bowl with vegetables and then add pasta, parsley, scallions, and remaining ½ cup of feta to bowl and toss to combine.
Serve in individual bowls with red hot pepper flakes and additional crumbled feta sprinkled over the top.