I totally agree that you could start from scratch, which might relate to starting with a cow when you have a recipe for grilling a steak, since there's a lot of extra steps you would need to take before getting to the stage when you could actually perform the steps of the recipe.
Here is a link describing true Tomato Paste and how/where it is made.
Tomato paste - Wikipedia, the free encyclopedia
Here is a recipe for making your own, but I have not tried it nor compared it to the commercial version:
Tomato paste lends depth and flavor to many dishes.
5 lbs plum tomatoes
1/4 cup extra-virgin olive oil, plus 2 tablespoons
Kosher salt, to taste
1. 1. Heat oven to 300°. Roughly chop tomatoes. Heat 1?4 cup of the oil in a 12" skillet over high heat. Add tomatoes and season lightly with salt; bring to a boil. Cook, stirring, until very soft, about 8 minutes.
2. 2. Pass the tomatoes through the finest plate of a food mill, pushing as much of the pulp through the sieve as possible, leaving the seeds behind.
3. 3. Rub a rimmed 13" x 18" baking sheet with remaining 2 tbsp. of oil; spread tomato purée evenly over sheet. Bake, using a spatula to turn the purée over on itself occasionally, until most of the water evaporates and the surface darkens, about 3 hours. Reduce heat to 250°; cook until thick and brick colored, 20?25 minutes.
4. 4. Store sealed in an airtight container in the refrigerator for up to one month, or freeze, wrapped well in plastic wrap, for up to 6 months.
Yield: 1 cup