Heat oil in a Dutch oven or large pot over medium. Add onion, anchovy fillets (if using), and ½ teaspoon salt; cook, stirring occasionally, until softened and starting to brown, about 5 minutes.
Stir in garlic, tomato paste, oregano rosemary, and red-pepper flakes; cook until mixture starts to caramelize, 2–3 minutes.
Mash ½ cup chickpeas then add to soup with remaining chickpeas, tomatoes and their juices, and broth; bring to a boil over high heat.
Reduce heat to medium-high, add pasta and simmer, stirring frequently to avoid scorching, until pasta is al dente, about 10 minutes. (If desired, add 1 cup water for a brothier soup).
Stir in kale and cook until wilted.
Season to taste with salt (at least 1 teaspoon) and black pepper.
Top each serving with grated Pecorino and a drizzle of olive oil.