Preheat the oven to 475 degrees.
In a large baking dish, add both kinds of tomatoes, bell pepper, garlic, and onion. Sprinkle with salt and pepper, oregano, and drizzle with olive oil.
Roast in the oven at 475 degrees for 20 minutes, then reduce the heat to 350 degrees and bake for an additional 15 minutes (this helps caramelize the veggies without burning them).
Remove from the oven and allow to cool for a bit. Squeeze the garlic cloves out of its head into the baking dish.
Add the vegetable mixture to a blender and blend until very smooth.
Transfer to a Dutch oven or saucepan on the stove over medium-high heat. Add in the chicken broth and bring to a gentle boil, then reduce the heat to low and allow to very gently simmer for 10-15 minutes, stirring often.
Pour in the heavy cream, allow to heat through, and serve.