Preheat the broiler. Melt 3 tablespoons butter in the microwave, then toss with the cauliflower on a baking sheet; season with salt and pepper. Broil until charred and just tender, 6 to 8 minutes; set aside.
Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 3/4 cup cooking water, then drain.
Meanwhile, melt 2 tablespoons butter in a separate large pot over medium-high heat. Add the panko and cook, stirring, until browned, 2 to 4 minutes; stir in the lemon zest and season with salt. Remove to a bowl and wipe out the pot.
Melt the remaining 6 tablespoons butter in the pot over medium heat. Cook, stirring occasionally with a rubber spatula, until brown flecks appear, 5 to 7 minutes. Stir in the anchovies, cauliflower, pasta, reserved cooking water and lemon juice. Cook, stirring, until slightly thickened, about 1 minute; season with salt and pepper. Divide among bowls and top with the toasted panko.