In a large, heavy bottomed pot, heat the olive oil over medium heat. Add in the onions and garlic and cook until the onions are translucent. About 5 minutes. Add in the carrots and cook until they just begin to caramelize, about another 5 minutes.
Stir in the flour until the vegetables are evenly coated, then add in one cup of vegetable stock to deglaze the bottom of the pan. Use your utensil to scrape up any stuck-on bits (fond) from the bottom of the pan. Stir until the flour has begun to dissolve from the vegetables, then add in the rest of the vegetable stock, the milk, and heavy cream.
Bring the soup to a boil and add in the broken lasagna noodles. Reduce the heat to a simmer and add the zucchini and yellow squash. Let simmer for 25 minutes, or until the lasagna noodles are cooked to al dente.
Stir in the cut ricotta cheese, parmesan, and asaparagus and cook until the asparagus turns bright green and is tender, about 5 minutes. Right before serving, add in the grape tomatoes and pesto until combined. Season with salt and pepper, and serve with a garnish of freshly grated parmesan and fresh basil.
While the soup is simmering, you have to keep an eye on the lasagna noodles to keep them from sticking together. If they do, they have a tendency to cook inconsistently as well as take longer to cook. If they do get stuck together, just use a utensil to separate them and continue cooking.