Preheat the oven to 225 degrees F. Line two cookie sheets with parchment paper.
Rinse the tomatoes and pat dry. Slice lengthwise and place on the cookie sheets, seed side up.
Pat the tomatoes with a paper towel to absorb some of the juice. Sprinkle with sea salt.
Bake at 225 degrees until dried and deep red - about 5-6 hours.
Check the tomatoes regularly after the 4-hour point. They will look wrinkled, dried, and rich red.
Some of them may dry faster than others, so you can remove those so they don't get burnt. Once they are all dried, dark red, and wrinkled, remove the pan from the oven.
Let cool completely. Store in in a glass jar with some olive oil, about 3-4 tablespoons. They can be stored safely for about a month in the refrigerator.