Preheat the oven to 425°F (220°C).
Arrange the fennel wedges on a baking sheet and drizzle with olive oil. Season generously with salt and black pepper.
Roast for 30–35 minutes, turning once halfway through, until the fennel is deeply golden, caramelized, and tender.
Meanwhile, bring a large pot of salted water to a boil and cook the pasta according to package directions until al dente.
Reserve ½ cup of pasta water before draining.
In a large skillet, warm a tablespoon of olive oil over medium heat.
Add the sliced garlic and cook until fragrant, about 1 minute.
Stir in the capers and crushed red pepper flakes and cook for another minute.
Add the roasted fennel to the skillet and gently break apart some of the wedges with a spoon.
Stir in the red wine vinegar and allow it to cook for 30 seconds.
Add the cooked pasta and a splash of reserved pasta water.
Toss until the pasta is evenly coated and the sauce becomes silky. Add more pasta water as needed.
Taste and adjust seasoning with additional salt and pepper.
Garnish with chopped fennel fronds and Parmesan cheese, if desired.
Serve immediately.