Bring a large pot of salted water to a boil. Cook the pasta until al dente according to package instructions. Reserve about 1 cup of pasta water before draining.

While the pasta cooks, heat olive oil in a large skillet over medium heat. Add the garlic and cook for 1–2 minutes until fragrant. Stir in the red pepper flakes if using.

Add the capers and about ½ cup of reserved pasta water to the skillet. Let it simmer for a couple of minutes to build flavor and begin forming the sauce.

Add the cooked pasta directly to the skillet and toss to coat. If needed, add more pasta water a little at a time to create a silky sauce.

Remove the pan from heat. Stir in the lemon zest, lemon juice, and Parmesan. Toss until everything is well combined and glossy. Add the arugula and toss again.

Season with salt and black pepper to taste. Serve immediately.