Fill a medium saucepan with about 3 to 4 inches of water. Salt the water and bring it to boil. Pour in the pasta and cook for 12 to 15 minutes, depending on how you like the texture of your pasta.

While the pasta is cooking, preheat the oven to 425 degrees F (220 degrees C), and line a baking sheet with parchment paper. Toss the tomatoes and 1 tablespoon of oil together with a pinch of salt. Roast for 15 to 18 minutes, or until this skins of the tomatoes start to shrivel. Some of the tomatoes may have burst at this point, but that's ok.

Caramelize the onions by heating 1 tablespoon of olive oil in a small pan. Once the pan is hot, toss in the onions and cook until they are well browned. Set aside.

In large saucepan, bring 3 to 4 inches of water to boil. When the water is boiling, pour in the broccoli and let it cook for 2 minutes only (unless you like mushy broccoli). This will remove the bitter bite of raw broccoli. After 2 minutes, pour the broccoli into a nice, cold ice bath to stop if from continuing to cook.

In a food processor, mix the onions, 2 and 1/2 cups of cooked broccoli, cheese, sour cream, garlic, salt, and basil leaves together until you get a creamy sauce.

In a large bowl, mix the pasta, broccoli pesto, the remaining cooked broccoli, tomatoes, and shredded chicken together. Serve with more shredded cheese and toasted pine nuts. Enjoy!