1 large bunch broccoli, cut into about 4 cups florets and 1 cup thinly sliced stems from close to the base
Kosher salt
Ice
1 pound spaghetti
1/2 cup extra-virgin olive oil
2 teaspoon red pepper flakes
6 cloves garlic, minced
Juice of 1/2 lemon
1 cup freshly grated Parmigiano-Reggiano