Prep and cook the pasta: Bring a large pot of generously salted water to a boil.
Toast the breadcrumbs: While the water heats, melt 1 tablespoon of butter in a medium skillet over medium heat. Add the panko and cook, stirring constantly, until golden and fragrant – about 3 minutes. Transfer to a small bowl and wipe out the skillet.
Cook the pasta: Add the mafaldine to the boiling water and set a timer for 2 minutes less than the package directions call for.
Add the broccoli: When the timer shows 2 minutes left, drop the broccoli florets into the pasta water. Cook until the pasta is al dente and the broccoli is bright green and tender-crisp.
Reserve the pasta water: Before draining, scoop out 1½ cups of the starchy pasta water. Drain the pasta and broccoli together in a colander. Do not rinse.
Build the sauce base: In the same large pot, melt the remaining 3 tablespoons of butter over medium heat. Add the garlic, lemon zest, and red pepper flakes. Cook for 30 seconds, until fragrant.
Create the emulsion: Whisk in ½ cup of the reserved pasta water and all the lemon juice. Let it bubble for 30 seconds. The liquid should look slightly cloudy and smell intensely lemony.
Bring it together: Add the drained pasta and broccoli to the pot. Toss vigorously with tongs for about 1 minute, adding more pasta water as needed to create a silky sauce that coats every ribbon. Remove from heat.
Add the cheese: Sprinkle the grated Parmesan over the pasta and toss again. Taste and adjust with salt or another squeeze of lemon. Serve topped with the toasted breadcrumbs.