Prepare Pasta Water: Heat a large pot of salted water to boil while you cook the beef.
Heat a large skillet to medium high heat. Add olive oil to the skillet and cook ground beef with 1 ½ teaspoon flaky sea salt and ground pepper for about 8 minutes until almost fully cooked.
Once the hot water is boiling in the pot, add the pasta and olive oil, cook until al dente (tender, but firm and chewy), about 11-13 minutes. The olive oil will help the pasta to not stick together. Stir every few minutes to keep pasta from sticking to the bottom of the pot.
While the pasta and beef are cooking, chop your broccoli into florets.
Drain the beef fat from the skillet. Add the minced garlic, calabrian chilis and white wine, sauté for 1 minute, keep the skillet on low heat.
Remove and strain the pasta and set aside for serving. I would ladle out the pasta and keep the pasta water to be used to boil your broccoli. You can add a dash of olive oil to the pasta to keep it from sticking while you finish preparing the dish.
Add your broccoli florets to your pasta water and cook for 3-5 minutes until slightly tender and they turn a bright green color. Before straining your broccoli, reserve 1 cup of pasta water for the sauce.
Add the pasta water, lemon juice, lemon zest, 2 tablespoon olive oil, parmesan cheese and spaghetti to the skillet. Stir for 2-3 minutes allowing the flavors to meld together. Add an additional ½ teaspoon of sea salt to taste. Add your broccoli florets around the edge of the skillet and top with more parmesan cheese. Enjoy!