Fill a medium-large pot with water (about 2-2.5 quarts) and bring to a boil over high heat. Season the water generously with salt (about 1 tbsp). Add the pasta and cook according to the package instructions. Reserve about 1 ½ cups of pasta water, then drain and set aside.
In a large skillet, warm the oil over medium-high heat. Once the oil is hot and shimmering, add the sausage, break it into chunks and let it cook, undisturbed, for about 2-3 minutes or until nicely browned. Continue to cook and break it up into smaller crumbles until cooked through with crispy bits, about 2-3 more minutes. Transfer to a paper towel lined plate or bowl.
To the skillet, warm a light drizzle of oil over medium heat (depending on how much oil is left in the pan, you just need a little bit). Add the tomato paste, garlic, and red pepper flakes and cook until the tomato paste darkens in color/caramelizes, about 2 minutes, stirring occasionally.
Stir in ½ cup of the pasta water, then add the broccolini. Cook for about 3 minutes or until the broccolini is crisp tender, stirring often. Add the sausage, pasta, cheese, and another ½ cup pasta water and cook, stirring often, until a glossy sauce forms and coats the noodles, about 2 more minutes. Add more pasta water, if needed to create more of a saucy consistency.
Serve topped with more parmesan, black pepper, and a squeeze of lemon.