BRING a large pot of salted water to a boil. Fill a large bowl with water and ice. Add asparagus to boiling water and cook until just tender, about 3 min. Drain and transfer to ice bath. Let stand until cold, 2 min. Drain, then dry with kitchen towel. Coarsely chop.
DROP garlic through the feed tube of a food processor while it’s running. Add asparagus, mint, parmesan, almonds, lemon juice, zest and salt. Pulse until finely chopped. With motor still running, pour in oils through feed tube and blend until smooth.