Finely mince garlic and mix together in a small bowl, anchovy paste, and salt. Whisk in vinegar and oil.
Cook rice in a pot with four cups of salted water for 13 minutes. Add asparagus and peas then cook for two more minutes. Drain and transfer to a medium-sized bowl.
Add vinaigrette, onion, and arugula and toss to combine. Season with salt and pepper, Let stand at room temperature for 30 minutes before service. Garnish with basil before serving.