First, prepare the vegetables. Dice the onion. Mince the garlic. Slice the celery. Peel and slice the carrots. Quarter the zucchini and squash. Trim and cut the green beans. Remove the green stalks from the leeks, slice the white end, and wash the sliced leek in a bowl of water to remove dirt. Remove the kale ribs and coarsely chop the leaves. Trim and slice the Brussels sprouts.
In a large dutch oven, heat the of olive oil over medium-high heat. Once the oil is hot, add the onion, garlic, carrots, and celery (mirepoix). Cook 4 to 5 minutes. Add the leeks and cook 1 minute. Add the broth and tomatoes. Season with basil, oregano, salt and pepper. Bring the soup to a boil, then reduce heat and simmer covered for 20 minutes.
During the last 10 minutes of simmering, bring a separate sauce pot of water to a boil. Add the pasta. Cook according to package directions, about 7 minutes, until al dente. Drain and set aside. Alternately, you can add the pasta to the soup 7 to 8 minutes before you are ready to serve. We recommend cooking pasta separately to prevent water logged, squishy pasta in leftover soup. Preheat the oven to 425°F.
At the end of simmer time, toss the sliced Brussels sprouts with avocado oil, garlic powder, salt and pepper. Spread the sprouts out on a large baking sheet. Cook for 8 to 10 minutes, tossing halfway through. The sprouts should be blackened in spots and crispy (but don't let them burn!). Remove from the oven and set aside.
While the Brussels sprouts cook, add the green beans, zucchini, and squash and cook 3 to 4 minutes. Add the kale and beans and cook another 1 to 2 minutes. Remove from heat. Divide the pasta among bowls. Ladle the soup over the pasta and top with prepared pesto, crispy Brussels sprouts, and Parmesan cheese.