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1
In a large stockpot, heat the 10 pounds plum tomatoes, covered, over high heat, stirring occasionally, until tomatoes dump their liquid. Bring to a boil in covered pot, stirring occasionally, and cook until tomatoes are softened, about 10 minutes.
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2
Preheat oven to 275u00b0F (135u00b0C) and grease several rimmed baking sheets and/or baking dishes with oil. Using a food mill or a stand mixer's vegetable strainer attachment, pass cooked plum tomatoes and all their liquid into a large heatproof container. Discard skins and seeds.
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3
Pour plum tomato puree into rimmed baking sheets and/or baking dishes, being careful not to overfill them.
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4
Carefully transfer baking sheets and dishes to oven and bake, checking every 15 minutes and stirring once puree begins to thicken, until a thick, spreadable tomato paste forms, at least 2 hours.
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5
Meanwhile, fill the same large stockpot with remaining 15 pounds mixed tomatoes and cook, covered, over high heat, stirring occasionally, until tomatoes dump their liquid. Bring to a boil in covered pot, stirring occasionally, and cook until tomatoes are softened, about 10 minutes. (Work in batches if your pot can't hold all 15 pounds at once.)
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6
Using food mill or stand mixer's vegetable strainer attachment, pass cooked mixed tomatoes and all their liquid into a large heatproof container. Discard skins and seeds. Measure out 1 quart (900ml) mixed-tomato puree and set aside.
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7
Heat 3 tablespoons (45ml) olive oil in a large, wide saucepan over medium heat until shimmering. Add onion and garlic and cook, stirring occasionally, until softened and sweet, about 8 minutes. Add remaining mixed-tomato puree and simmer, stirring occasionally, until reduced to a sauce-like consistency, 35 to 40 minutes.
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8
Remove from heat; stir in basil and tomato-plant cutting, if using; and let steep for 5 minutes. Discard basil and tomato-plant cutting. Stir in oven-dried tomato paste and reserved tomato puree and season with salt. Use as desired or freeze.
