Bring a large pot of salted water to a boil. Dust a baking sheet with flour.
For the pasta: Put the flour and pumpkin puree in a food processor and pulse in short bursts until the mixture comes together and a dough forms, about 1 minute.
Turn the dough out onto a floured work surface. Divide into 4 equal pieces. Roll and cut the pasta to desired thickness using a rolling pin or a pasta machine. Cut into the desired shape, transfer to the prepared baking sheet and sprinkle with flour (this keeps the pieces from sticking together). Cover the pasta with plastic wrap for up to 4 hours if you are not cooking right away
Cook the pasta until tender but not mushy (there shouldn’t be a line of raw flour in the center), 2 to 5 minutes, depending on the thickness and shape. Drain thoroughly.
For the sage butter: Meanwhile, melt the butter in a large skillet over medium heat. Add the sage and cook, stirring occasionally, until the leaves are crispy and the butter begins to brown slightly and has a nutty aroma. Sprinkle in 1 teaspoon of salt. Add the drained pasta to the skillet and toss vigorously to coat. Season with salt and pepper.