Simmer on low heat for 2-3 hours or until cooked down and starting to darken.
Add carrot piece for the last 30 minutes to absorb acidity.
Remove sprigs of herbs, bay leaves, and piece of carrot.
Optional: Use an immersion blender to puree sauce until smooth (for a thicker sauce, skip this step).
Use fresh or store in the refrigerator up to 1 week, or can it according to your canner's instructions for tomato products.
Notes
To peel fresh tomatoes (or peaches) cut a small "x" on the top and drop into boiling water for 10 seconds and then drop into an ice bath. The skin will easily peel off.