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Heat oven to 415 degrees.
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Wash and dry the tomatoes. Slice in half.
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On a very large sheet pan (cookie sheet) spread some olive oil and place the tomatoes cut side down.
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Add the sliced onions and sliced carrot.
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Add a generous tablespoon of olive oil and using your hands make sure to coat everything. Then spread everything out in a single, even layer, making sure to space the tomatoes evenly and not crowd to the centre.
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Sprinkle everything with salt, pepper and red pepper flakes.
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Add the thyme sprigs or sprinkle the dried thyme.
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Roast in the oven for 40 - 60 minutes, moving things around with spatula if the outer edges begin to burn.
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You want the tomatoes to release their juices and the onions and carrots to get very soft.
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Remove from oven.
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If pureeing in the blender (or food processor), using tongs remove the tomato skins and then transfer everything, including any juices on the tray to the blender and process until desired smoothness. Adding pasta water to thin as desired (now or when reheating).
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Alternately put the entire mixture through a food mill skins and all.
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Mix with cooked pasta and serve. Or transfer to an airtight container and refrigerate or freeze.