Core the tomatoes, cut them in half lengthwise, and scrape out seeds with fingers. Put the tomatoes in a 12-quart stainless stockpot, and, stirring from time to time, bring to a boil over medium heat. Then reduce the heat to a simmer and let the tomatoes cook until soft -- about 30 minutes.
Place a food mill over a large bowl. Working in batches, process the tomatoes to remove skins and any remaining seeds from the pulp and juice.
Pour the pulp and juice into a 4 or 5 quart non-reactive pot, and bring to a boil over high heat. Then reduce the heat to a simmer, and cook until the liquid thickens and reduces by about half -- 30 minutes to 1 hour.
Center the oven rack, and, using the convection setting if available, preheat the oven to 200°F.
While the oven is heating, line a large, rimmed baking sheet with 2 or 3 layers of baking parchment. Pour the sauce over the paper. Spread the sauce with a silicone spatula so it covers the entire pan.
Put the sauce in the oven, and let it cook for 30 minutes. Stir the sauce briefly with the spatula, and then return it to the oven for another 30 minutes. Stir again, and then scrape the sauce towards the center of the pan to form a rough rectangle.
Working in 30 minute intervals, continue to cook, stir, and form the sauce into a rectangle until all liquid has evaporated -- 3 to 5 hours in total. The rectangle will decrease in size as evaporation occurs. The paste is done when liquid no longer seeps along the edge of the rectangle.
Let the condiment cool to room temperature on its pan. Then transfer to a pint-size jar, and film the surface with a little olive oil. Covered and refrigerated (and filmed with olive oil after each use), the paste will remain fresh and wonderful for several months.