Heat 2 tablespoon olive oil in a large skillet over medium. Add garlic and red pepper flakes; cook 90 seconds until fragrant but not browned.
Add broth and bring to a boil. Add halved linguine and stir to prevent clumping. Reduce to a vigorous simmer.
Add broccoli florets, pressing into the liquid. Cover and cook 10–12 minutes, stirring every 3–4 minutes, until pasta is almost al dente.
Season shrimp with salt and pepper. Nestle into the pasta. Cover and cook 2–3 minutes until pink, opaque, and loosely curled.
Remove from heat. Drizzle with remaining 1 tablespoon olive oil, lemon juice, and lemon zest. Toss gently.
Serve immediately topped with parsley and Parmesan.
