Bring a large pot of heavily salted water to a boil over medium-high heat.

While the water is coming to a boil, trim the stems and slice the snap peas, and cut off the hard ends of the asparagus stems and cut the rest into 1/4-inch-thick pieces; leave asparagus tips whole. Finely chop the garlic. Grate the parmigiano-reggiano.

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 (1 to 3 minutes for fresh pasta, more for dried pasta). Drain well and transfer pasta to a large bowl. Immediately toss pasta with vegetables, Parmigiano-Reggiano, crème fraîche and herbs (finely chopped). Season generously with salt and pepper, if needed.