Heat oil in a medium pot over medium. Add onion and cook, stirring occasionally, until softened and translucent, about 4 minutes.
Add garlic, thyme, rosemary, black pepper, red pepper, and ½ teaspoon of the salt; cook, stirring constantly, until garlic is softened and fragrant, about 1 minute.
Add tomato paste to pot; cook, stirring constantly, until paste is slightly darkened and completely coats onion and garlic, about 1 minute.
Add white wine; cook, scraping up any browned bits from bottom of pot, until slightly thickened, about 1 minute.
Add chickpeas to pot, and mash about one-third of chickpeas using back of a spoon or spatula.
Add vegetable broth; sprinkle with remaining 1 teaspoon of salt, and bring to a boil over high.
Stir ditalini into mixture in pot, and reduce heat to medium-low. Simmer, stirring occasionally, until pasta is tender, about 10 minutes.
Remove and discard thyme and rosemary sprigs from pot.
Stir in kale and Parmigiano-Reggiano until kale is wilted and broth is slightly thickened, 2 to 3 minutes.
Remove from heat. Divide evenly among 6 bowls; garnish with additional black pepper, red pepper, and Parmigiano-Reggiano.
