Bring a large pot of salted water to a boil, then add your pasta and cook until just al dente, about 9 minutes. Drain, reserving a small cup of pasta water, and set aside.
In a dry skillet over medium heat, toast the breadcrumbs until golden and crispy, about 3-4 minutes. Shake the pan frequently to prevent burning. Once done, transfer to a plate and set aside.
Using the same skillet, add a tablespoon of olive oil and toss in the raw broccoli florets. Cook for 2-3 minutes until bright green and slightly crisp, then remove from heat and set aside.
In a small saucepan, gently heat the heavy cream over low heat. Add the minced garlic and cook until fragrant, about 1 minute, stirring frequently to avoid burning.
Return to your drained pasta in the large pot or a bowl. Pour the warm cream and garlic mixture over it, then sprinkle in the grated Parmesan cheese. Stir gently to coat the pasta evenly, adding a splash of reserved pasta water if the sauce feels too thick and to achieve a silky consistency.
Fold in the raw broccoli florets into the pasta, allowing the residual heat to slightly soften them while keeping their crunch.
Season with salt and pepper to taste, and add a generous amount of lemon zest for brightness. Toss everything gently to combine.
Serve the pasta in bowls, sprinkle the toasted breadcrumbs on top for crunch, and finish with a drizzle of olive oil. For an extra zing, add a little more lemon zest if desired.
Enjoy immediately while the breadcrumbs are crispy and the broccoli remains fresh and crunchy.
