Pasta e Ceci Soup

3 Tbs. plus 1/2 cup extra-virgin olive oil 

2 carrots, finely diced 

1 large yellow onion, finely diced 

1 1/2 tsp. minced garlic 

1/3 cup diced tomato 

1 1/4 cups dried chickpeas, soaked in water overnight, drained and rinsed 

6 cups water 

2 fresh thyme sprigs 

1/4 cup vegetable oil 

3 fresh rosemary sprigs, cut into 1 1/2-inch lengths 

Kosher salt, to taste  

1/2 lb. tubetti pasta, cooked until al dente and drained 

Freshly ground pepper, to taste 

Shaved Parmigiano-Reggiano cheese for serving