How to Make It
Preheat oven to 400°F. Cut stalk from broccoli head; peel and thinly slice into rounds. Cut crown into florets and toss with stalk, garlic, 1 tablespoon oil, ¼ teaspoon salt, and ⅛ teaspoon pepper on a rimmed baking sheet. Roast until charred in spots, stirring halfway through, about 20 minutes.
Meanwhile, bring a large pot of generously salted water to a boil. Add pasta and cook according to package directions. Drain, reserving 1 cup pasta water. Set aside.
Place 1 cup roasted florets in a large bowl; transfer remaining to a food processor. Add reserved pasta water, almonds, cheese, lemon zest, lemon juice, 1 cup arugula, and remaining 2 tablespoons oil, ½ teaspoon salt, and ⅛ teaspoon pepper. Process until pesto is smooth, about 1 minute.
Transfer pasta to bowl with florets. Toss with pesto and remaining 2 cups arugula. Top with more cheese, if desired.