Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 3/4 cup cooking water, then drain.
Meanwhile, heat 2 tablespoons olive oil in a large nonstick skillet over medium-high heat. Add the artichokes and season with salt. Cook, turning halfway through, until browned, about 5 minutes. Transfer to a plate.
Add the remaining 2 tablespoons olive oil, the garlic and beans to the skillet. Cook, stirring occasionally, until the garlic is golden, about 2 minutes. Stir in the cherry tomatoes, red pepper flakes and 1/2 teaspoon salt. Bring to a simmer; cook, stirring occasionally, until slightly thickened, about 3 minutes.
Add the pasta and the reserved cooking water to the skillet. Cook, stirring, until the pasta is coated, about 1 minute. Stir in the parsley, parmesan and artichokes; season with salt and pepper. Drizzle each serving with olive oil and top with more parmesan.