Heat 3 Tbsp. oil in a large saucepan over medium. Add onion and season with salt. Cook, stirring occasionally, until onion is beginning to soften, about 5 minutes. Add garlic and continue to cook, stirring occasionally, until onion and garlic are both very soft and just beginning to brown around the edges, 5–6 minutes longer. Add rosemary and red pepper flakes and cook, stirring, until fragrant, about 30 seconds.

Add chickpeas and tomatoes and cook, stirring occasionally, until tomatoes are slightly thickened, 6–8 minutes.

Add pasta and 4 cups water. Increase heat to medium-high, bring to a simmer, and cook, stirring occasionally to prevent pasta from sticking, until pasta is al dente, 13–16 minutes depending on shape. Stir in parsley and 3 Tbsp. Parmesan; season with salt.

Divide brothy pasta between bowls. Drizzle with more oil and top with Parmesan and black pepper.