Prep the pumpkin, depending on what you have. If it is whole, cut it in half from top to bottom and scoop out the seeds with a spoon: no need to peel it. If you bought it pre-cut, there is nothing to do.
Onto the baking sheet, on parchment paper. The halves go cut side down. Loose pieces go in a single layer, not touching: crowded together they steam in their own moisture and the puree comes out wetter.
Roast at 200 °C (400 °F). Halves take 45 to 60 minutes. Pieces take 40 to 50 minutes. It is ready when a knife slides in with no resistance at all.
Scoop out the flesh. If you roasted halves, flip them, let them cool for a few minutes, and scrape the flesh out with a spoon all the way to the skin. Pieces go straight into the blender.
Blend until completely smooth.
Push it through a fine-mesh strainer with a spatula to remove the fibers. It takes about five minutes and it is what gives the puree its silky texture.
Into the skillet. Use the widest one you have, over medium low heat, stirring often. 15 to 25 minutes depending on how watery the pumpkin was, and a few more if you roasted halves. It spatters like lava, so keep a lid half on between stirs or turn the heat down.
Check it with the spatula test. Drag the spatula across the bottom: if the trail takes a second to close, it is done. If it closes right away, keep going.
Weigh it. 1.2 kg (2.6 lb) of pre-cut pumpkin gives you about 650 g (2⅔ cups) of thick puree, which is about 1½ cans. If your recipe calls for a specific amount, weigh out what you need and save the rest.
Let it cool completely before storing it, and before using it in any cold recipe like a no-bake cheesecake. Spread out on a sheet pan or a plate, it cools in about 30 minutes; in a deep container it can take a couple of hours. For soups or quick breads you can use it warm.