Prepare your gnocchi dough. Make your gnocchi dough according to your chosen recipe. Lightly flour a clean work surface or wooden board, then transfer your gnocchi dough onto it. Line a plate or tray with parchment paper (you'll place the shaped gnocchi on here).
Roll and cut your gnocchi dough. Shape your dough into a rough rectangle, then slice off a (roughly) 1-inch piece from the short end. Roll the piece into a long rope, then slice it into small pieces, about 1 to 2 inches long. Roll each piece into a ball, then gently flatten into a disc.
Shape the gnocchi into pumpkins. Use a piece of kitchen string to press gentle grooves around each disc, working your way around, to create lines that make the gnocchi resemble a cute little pumpkin. If any pieces flatten, cup your hands around them to round them back into shape. Place the pumpkin-shaped gnocchi onto the prepared tray or plate.
Make your sauce. The gnocchi will only take a couple of minutes to cook, so make sure you have your sauce ready to go. For the brown butter and crispy chorizo sauce: add the chorizo to a high-sided pan or skillet, then set the heat to high. Cook, stirring, for a couple of minutes, until super crispy. Transfer to a plate, but keep any chorizo oil in the pan. Add 4 tablespoons of butter and let it melt, stirring as it foams, develops little brown spots, and smells gorgeously nutty. This is your brown butter. Remove the pan from the heat.
Cook the gnocchi. Bring a large pot of well-salted water to a boil, then carefully drop in the gnocchi. Cook for a couple of minutes, until the gnocchi float to the top of the water. At this point, they’re ready to add to your sauce.
Add the gnocchi to the sauce. Use a slotted spoon to transfer the cooked gnocchi straight into the pan with your sauce, along with a little gnocchi cooking water (about ¼ cup - this helps to form a lovely luscious sauce). Turn the heat back on to medium, then toss the gnocchi through the brown butter, letting it sit undisturbed on one side for a few minutes, to crisp up the bottom.
Finish the sauce and serve. Continue to gently toss the gnocchi through your sauce until it's silky and glossy. Divide the gnocchi between plates, making sure to spoon over lots of the lovely brown butter sauce. Drizzle the gnocchi with the chili crisp, then scatter over the crispy chorizo. Finish with grated parmesan and the chives. Enjoy right away.