Heat a large pot over medium heat. Once hot, heat up oil. Then add onion, garlic, carrots, and celery (and/or other leftover veggies). Add 1/2 tsp each sea salt and black pepper and stir to coat. Sauté for about 5 minutes, stirring frequently, until softened and slightly browned.
Add water, parsley, thyme, rosemary, bay leaves, 3 tsp sea salt and black pepper and 1/2 tsp cayenne pepper and increase heat to medium high until the mixture comes to a boil. Once boiling, reduce heat to a simmer and add tomato paste (add less for less intense flavor, or more for more robust flavor!). Stir to combine and cover with the lid cracked.
Continue cooking for at least 1 hour 30 minutes, preferably 2 hours. The flavor will deepen the longer it cooks.
Near the end of cooking, taste and adjust flavor as needed, adding more herbs for an earthy flavor, salt for saltiness, (cayenne) pepper for a little spice, or tomato paste for depth of flavor. In total, I added about 3 tsp sea salt and 1 tsp black pepper and 1 tsp of cayenne pepper and all of the suggested amount of tomato paste.
Let cool slightly before pouring over a strainer into another pot. Then divide into smaller portions to freeze. Let cool completely before sealing. Store in the refrigerator up to 5 days or in the freezer up to 1 month (sometimes longer).