Roast: Position a rack in the center of the oven and preheat the oven to 375ºF. Place the tomatoes, onions, garlic, and carrots on one large baking sheet. It’s okay if some of the ingredients are overlapping. Drizzle the olive oil along with a generous pinch of salt and pepper and give it a good toss so it’s all evenly seasoned. Place the baking tray in the oven and allow the ingredients to bake for 1 hour. Check on the ingredients around 30 minutes and give it a toss as needed.
Blend: Transfer the ingredients along with any juices from the baking tray to a blender and blend the veggies until they are completely smooth. If you’ve got a super powerful blender it will go in one batch and be super quick. If you’ve got a regular blender, you may need to add a little broth to help it along. If you’ve got a hand blender, you can skip this step and add all the remaining ingredients into a large pot and just blend it all there.
Soup: Transfer the puree into a large dutch oven over medium heat. Add the chicken broth and allow the soup to heat all the way through, about 5-7 minutes. Add the balsamic vinegar and red pepper flakes. Add two tablespoons of the pesto and give the soup a taste. If desired, add more. I used 4 in total because I love a little extra punch of basil. Season with additional salt and pepp as desired. Serve with cheese toasts.