Rinse the tomatoes well, remove the stems, and cut into chunks.
Fill a blender jar with the tomato chunks and blend until the tomatoes have all reduced to a fine sauce.
To strain out the seeds and skin, place a mesh strainer or food mill over a large pot on the stove (or over the crock of a slow cooker pot). Pour the tomato sauce into the strainer. Use a sspoon or a spatula to press the tomato sauce through the strainer into the pot below.
Repeat with the remaining tomatoes. If you want to add red peppers or other vegetables, now is the time to do it.
Stovetop
Heat the sauce over low to medium heat until simmering. Occasionally stir it and check on the consistency. As the water evaporates, the sauce will thicken. As it thickens, turn the heat down and check on the tomato paste more often. (It's more likely to burn as it gets thicker and has less water.)
Slow cooker
Cook the tomato sauce in the slow cooker on low with the lid off. In the slow cooker, you can leave the tomato paste unattended for longer periods of time. Still, as it starts to thicken, you will also need to check on it more often to prevent it from burning.
In the oven
To give the tomato paste a more caramelized flavor, and reduce it even further, you can bake it on clean baking pans on low heat in the oven. Occasionally use a spatula to scrape the tomato paste from the bottom of the tray with a spatula and stir it, while checking on the consistency. Some people choose to do the entire process of making the tomato paste in the oven, but I prefer to reduce it to a thick sauce on the stove first.
Once you've achieved the desired consistency, the tomato paste is ready to be used in recipes, or ready to be stored.
Video
Notes
Making your own tomato paste takes a bit of time, but it's totally worth it. You can then use it in soups, sauces, or add it to ground beef for homemade tacos, etc.
Yield
Makes around 18 ounces.
Adding other vegetables
Some people like to add red peppers, onions, or other vegetables to their tomato paste. I prefer to keep things simple and just use tomatoes and add in the desired vegetables, spices, and seasonings when making a recipe with the tomato paste.
Storage
It can be stored in the fridge for 7-10 days or even longer if the paste was reduced enough. It can also be canned or frozen. (Add some citric acid (which can be in the form of a bit of lemon juice) to the paste before canning. If it's concentrated enough, it may not need it.)Freezing in perfectly cube-shaped ice cube trays is a great way to save space in the freezer. (The cubes can be stored in freezer bags.)