Bring a large pot of heavily salted water to a boil over medium-high heat. While the water is coming to a boil, slice snap peas and asparagus stems into 1/4-inch-thick pieces; leave asparagus tips whole.
Melt butter in a large skillet over medium-high heat. Add snap peas, asparagus, English peas, and onion. Cook until vegetables are barely tender (but not too soft or mushy), 3 to 4 minutes. Stir in garlic and cook 1 minute more. Season with salt and pepper; set aside.
Drop pasta into boiling water and cook until al dente. Drain well and transfer pasta to a large bowl. Immediately toss pasta with vegetables, Parmigiano-Reggiano, crème fraîche and herbs. Season generously with salt and pepper, if needed.