Bring a large pot of salted water to a boil and cook the angel hair pasta according to package instructions until al dente; reserve about 1/2 cup of pasta cooking water, then drain.
While the pasta cooks, heat the olive oil in a large sauté pan over medium-high heat until shimmering.
Add the chopped garlic and diced shallots and sauté about 1 minute, until softened and fragrant.
Add the spiralized or julienned zucchini to the pan, season with kosher salt and black pepper, and cook about 1½ minutes, stirring frequently.
Stir in the diced tomatoes, crushed red pepper flakes, chopped parsley or basil, and the broth; adjust salt and pepper, and cook about 1 more minute to warm through.
Remove the pan from heat, add the drained pasta to the vegetables and toss well; add reserved pasta water as needed to loosen the sauce.
Serve immediately, seasoning with additional salt and pepper to taste and grated Parmesan if desired.