Preheat oven to 300 degrees Line a large baking sheet with foil.

Slice tomatoes in half or quarters, making them all roughly the same size.  Chop carrots in half lengthwise and then in 1-2 inch pieces.  Chop onion in large pieces, about 1-2 inches.  Place everything on baking sheet and drizzle with olive oil and sprinkle with salt and pepper.  Arrange everything in a single layer, with tomatoes sitting skin-side down. Cut top 1/3 of whole garlic head off and discard.  Place garlic on a piece of foil and drizzle with olive oil and sprinkle with salt and pepper. Pull sides of foil up and secure.  Place foil pack on baking sheet with tomatoes.

Roast in the oven for 2-3 hours, until everything is tender and tomatoes appear slightly shriveled.  (In my oven it almost always takes 2 1/2 hours).

Remove from oven and let cool slightly.  Place roasted vegetables in a food processor with broth.  Open garlic packet and squeeze all cloves into the food processor.  Pulse several times and then add fresh herbs.  Pulse again until desired consistency is reached.  Season with salt and pepper, add additional broth for consistency.  If needed, add a little sugar, or a drizzle of balsamic vinegar.  Let cool completely and then store in the fridge for a few days, or in the freezer for several months.    Yields 2-1/2 cups sauce.