Prep. Remove the stems, tips, green cores, and any black spots or discolorations from the tomatoes. Chop into 1/2" (1.3 cm) cubes. Chop the onions and mince or press the garlic.
Cook. Mix everything together in a pot and simmer for 1 hour with the lid off so it will reduce and thicken. Stir periodically to keep it from burning.
Strain. Force it through a food mill, chinois, or mesh strainer to remove the seeds and other solids. If you are using a mesh strainer, a ladle makes a good pusher. .
Simmer. Put the ketchup back on a burner and simmer, lid off, until it is thick, like ketchup. Taste it and adjust any seasonings to your taste.
Bottle it. Let cool then pour into a squeeze bottle, and chill. Keep refrigerated.