Bring a large pot of generously salted water to a boil. Add the pasta and cook according to package directions until al dente. Before draining, reserve about 1 cup of the starchy pasta water. Drain the pasta and set aside.

While the pasta cooks, heat olive oil in a large skillet or Dutch oven over medium heat. Add the minced garlic and diced shallot. Sauté for 3-4 minutes until softened and fragrant, being careful not to brown the garlic.

Add the roughly chopped green olives and red pepper flakes to the skillet. Cook for another 2-3 minutes, stirring frequently, allowing the flavors to meld.

Pour in the undrained diced tomatoes and vegetable broth (or some of the reserved pasta water). Bring the sauce to a gentle simmer, then reduce heat to low, cover, and let it cook for 10-12 minutes, allowing the flavors to deepen. Stir occasionally.

Uncover the skillet. Stir in the chopped fresh parsley, salt, and black pepper. Taste and adjust seasonings if necessary, remembering that olives are quite salty. If the sauce is too thick, add a little more reserved pasta water until it reaches your desired consistency.

Add the cooked, drained pasta directly to the skillet with the sauce. Toss everything together until the pasta is evenly coated. Serve immediately, garnished with extra fresh parsley and grated Parmesan cheese, if desired.