Preheat oven to 400°F (205°C).
Bring a large pot of well-salted water to boil over high heat.
Meanwhile, in a small bowl, combine the panko, parsley, if using, thyme, red pepper flakes, 1/4 cup (25 g) of the Parmesan, the lemon zest, and 1/4 teaspoon salt.
In a small skillet over medium-low heat, or in a microwave-safe dish in the microwave, melt 2 tablespoons of butter. Pour over the panko mixture, and toss to coat.
Cook pasta in the boiling water for 2 minutes less than the al dente time indicated on the package. Add the broccoli and cook until it is crisp-tender and the pasta is al dente, about 2 minutes more. Drain the pasta and broccoli in a colander. Add remaining 2 tablespoons of butter to the pot and melt over medium heat. Whisk in the flour and cook, whisking, until the mixture begins to bubble, about 1 minute. Gradually whisk in the milk, about 1/3 cup (80 ml) at a time, whisking until smooth between additions. Bring to a simmer, whisking, and cook, stirring occasionally, until the sauce is slightly thickened, about 5 minutes.
Remove from the heat, add the mozzarella, remaining 1/2 cup (50 g) Parmesan, and 1 teaspoon salt, and whisk together until the cheese is mostly melted (the mozzarella may not fully incorporate into the sauce; this is okay).
Add the pasta, broccoli, and lemon juice, if using, to the sauce and toss to combine. Dump into a large cast-iron skillet or 2-quart (2 L) baking dish and top with the bread crumb mixture.
Bake until the pasta is bubbling and the bread crumbs are golden brown, 15 to 20 minutes. Remove from the oven and let stand for 5 to 10 minutes to allow the sauce to thicken before serving.