Cook the pasta in a pot of boiling salted water until just shy of al dente. Reserve about 1 cup of pasta water and drain the rest.
Heat the olive oil in a large pan over medium-high heat before adding the broccolini. Cook for 3-4 minutes, tossing once or twice, until nicely roasted (vibrant green with browning in spots). Transfer to a bowl and set aside.
Add the ground chicken to the same pan and cook for 2-3 minutes until golden brown on one side. Use a spatula to break the chicken apart but don't over-mince. I like leaving the chicken in small bite-size chunks. Once the chicken is cooked through, add the sauce and cook until it begins to thicken, another 1-2 minutes.
Add the broccolini to the pan with the chicken and toss together.
Add the cooked pasta, grated parmesan, lemon zest, and about ½ cup of the reserved pasta water. Toss together until a smooth sauce coats everything. Use more pasta water if needed.
Finish with a squeeze of lemon juice, black pepper and/or chili flakes, and extra parmesan or a drizzle of olive oil, if desired.