In a large pot, add the heirloom tomatoes, cherry tomatoes, and fire-roasted tomatoes, and bring to a boil. Once boiling, turn heat to low-medium and let simmer, stirring occasionally.
Place a medium-size sauté pan over medium heat. Add the onion and carrot, cover with a lid, and stir occasionally.
Once the onions start to become translucent, add the mushrooms and broccoli. Keep covered and let them sauté for 5 more minutes. If the veggies start to stick to the bottom of the pan, add a little water as needed.
Once the tomatoes are broken up and the sauce has a semi-chunky consistency, add the veggies and dried herbs to the pot of tomatoes. Stir well. Let pasta sauce simmer for 15 more minutes and then add any fresh herbs you may be using.
Blend the sauce using an immersion blender, which is hand-held and fits right into the pot. Pulse the immersion blender a few times until you have the consistency you desire. If you don’t have an immersion blender, transfer part of the sauce to a blender, blend until smooth, and then pour it back into the pot.
Let the sauce continue to cook until it is your desired thickness. The longer it simmers, the thicker it will become. Serve over whole grain pasta, winter squash, or another unprocessed starch.