Place a fine-mesh strainer over a bowl and pour the tomatoes into the strainer. Shake them back and forth a bit until they settle, then let them drain for 1 hour. You will be left with the tomatoes in a thick puree. The strained liquid can either be discarded, or used in a Bloody Mary, your call. 

Over a bowl, gently puncture the bottom or side of each tomato with your thumb and push out the seeds so they fall into the bowl. Remove as many of the seeds as possible (you won’t get them all, and that’s OK), doing your best not to discard any of the tomato flesh or thick puree.

Combine the tomatoes, thick puree from the strainer, oil, garlic, and ½ teaspoon salt in a food processor or blender. If using a food processor or regular blender, pulse multiple times until smooth. If using a high-powered blender, blend on a low setting until smooth. If you blend it too intensely for too long, you’ll incorporate air bubbles into the sauce, thus diluting the flavor.