Blanch asparagus in salted boiling water for 2–3 minutes, adding snap peas for the final minute. Transfer to ice water, then drain and pat dry.

For pesto, pulse mint, parsley, almonds, Parmesan, lemon juice, and a pinch of salt. Stream in olive oil until spoonable; add a little water if needed.

Cut asparagus into bite-size pieces. Toss with snap peas, peas, and radishes in a large bowl.

Spoon mint pesto over the vegetables and toss lightly. Taste for salt and lemon, then serve chilled or at room temperature.