Finely mince garlic and anchovies together with 1 teaspoon salt on a cutting board until a paste forms. Transfer to a bowl; whisk in vinegar and oil.
Cook rice in a pot of salted boiling water until tender, about 13 minutes. Add asparagus and peas; cook until crisp-tender, about 2 minutes. Drain and transfer to bowl with vinaigrette.
Add onion and radicchio, toss to combine, and season with salt. Let stand 30 minutes. Add basil, toss to combine, and let stand 30 minutes more before serving.