Pre-heat oven on broil.
Toss cauliflower florets with 2 tbsp. oil, salt, and pepper on a baking sheet; broil until charred and tender, 8–10 minutes.
Heat 1⁄3 cup oil in a high-sided skillet over medium-high. Cook capers until crisp, 6–8 minutes. Using a slotted spoon, transfer capers to paper towels to drain.
Cook breadcrumbs and chili flakes in the same skillet until crisp, 3–4 minutes; transfer to a plate.
Wipe skillet clean and melt butter over medium; cook until butter is a deep golden brown, 6–8 minutes. Stir in mustard, salt, and pepper; transfer to a bowl. Add remaining oil to skillet; heat over medium-high. Cook garlic, salt, and pepper until golden, 3-4 minutes.
Bring a large saucepan of very salted water to a boil. Check out pasta package for cooking times. Cook a few minutes before the it reaches dente status; times will vary based on pasta.
Drain pasta; add to skillet with half the reserved breadcrumbs, all the mustard butter, and half the parsley; toss.
Top with reserved cauliflower florets; garnish with reserved capers and the remaining breadcrumbs and parsley.