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Fill a 6-quart stockpot with water, add the kosher salt, and bring to a boil. Add the pasta, stir, and cook until al dente according to package instructions.
While the pasta cooks, pour the frozen broccoli into a 4-quart saute pan and cook, covered, over medium heat until the broccoli thaws, about 5 minutes.
Stir the olive oil into the broccoli and cook for 2-3 more minutes until the broccoli is tender.
Drain the cooked pasta and return to the stockpot. Transfer the broccoli to the stockpot, add the lemon zest, lemon juice, and the Parmesan and toss to mix evenly.
Season to taste with extra kosher salt and olive oil before serving, and pass extra Parmesan at the table, if desired.