Spiralize the zucchini, according to manufacturer's instructions, and set aside.
In a large skillet, heat the olive oil over medium-high heat. Add the asparagus and cook until tender, about 5 minutes. Stir in the peas and cook for 2 minutes. Add the zucchini noodles and cook for 1 minute, just so the noodles are warmed. You don't want to really cook them or they will get soggy. Remove from heat and pour the basil vinaigrette over the zucchini noodles. Toss with tongs until the noodles and vegetables are evenly coated. Season with salt and freshly ground black pepper, to taste. Serve immediately.