Spaghetti Alla Primavera

This dish called to me from the cover of my brother-in-law's Saveur magazine and it was as good as it looked. It was one of 150 classic recipes in the 150th issue, and I bet some of the other 149 would be worth trying. This is supposed to be from the New York City restaurant Le Cirque.

Spaghetti Alla Primavera 

slightly adapted from Saveur, October 2012

6 T olive oil
3 cloves garlic, minced
1 bunch asparagus, trimmed and sliced in 1- to 2-inch sections (I've used frozen green beans, broken up, in place of this and/or the broccoli depending on what I have)
1 C small broccoli florets
½ C frozen peas
1 lb. spaghetti, cooked al dente
1 C heavy cream
⅔ C grated Parmesan plus extra for the table
2 T unsalted butter
Kosher salt and pepper, to taste
1 C grape tomatoes, halved
2 T thinly shredded basil
½ C lightly toasted pine nuts

Heat 5 T oil in a 12" skillet over medium heat. Add 2 cloves minced garlic; cook until golden, about 2 minutes. Add asparagus, broccoli, and peas (or other choice of spring vegetables); cook 3 minutes. Add pasta, cream, Parmesan, and butter, season with salt and pepper, and toss to combine; transfer to a platter.

Bring remaining tablespoon oil and 1 clove minced garlic, tomatoes, and basil to a simmer over medium heat; pour over pasta; garnish with nuts. Serve with extra grated parmesan.