Scoop out the seeds from the 10 pounds very ripe plum or regular tomatoes with your fingers.

Dump the tomatoes in a wide 8-quart stainless steel or enamel pot and bring to a roiling boil, stirring occasionally, until the tomatoes release their juices, soften, about 30 minutes.

Place a food mill fitted with a fine disk over a large bowl and mill the tomatoes to remove the skins and any MIA seeds.

Pour the tomato purée back into the same pot and bring it back to a boil over high heat.

Lower the heat to medium-ish, and simmer, stirring frequently, until the purée has reduced to about 1 quart (946 ml), 45 to 90 minutes depending on the type and water content of your tomatoes.

Stir in the kosher salt, a teaspoon at a time, and taste. Add up to 2 tablespoons or more to suit your taste.

Preheat the oven to 200ºF (93ºC). If you have convection, now's the time to use it. Position a rack in the center.

Line an 18-by-13-inch rimmed baking sheet with a silicone baking sheet or parchment.

Spread the thickened tomato purée in an even layer with a spoon or spatula. It should cover the entire baking sheet.

Slide the baking sheet into the oven and roast for 30 minutes.

Remove the sheet and stir the purée with the spatula. Respread the purée into a rectangle about ⅛ inch thick.

Slide the baking sheet back into the oven and continue roasting until the tomato purée is quite thick, stiff, and a little sticky, about 3 more hours, stirring and respreading the purée every 20 minutes.

Let the paste cool to room temperature.

Spoon the paste into a clean canning jar, pressing it down to remove air pockets, which can spoil the paste.

Cover the surface with ½ inch olive oil so that the paste is submerged. Screw the lid on the jar and refrigerate.