Slice the pumpkin and remove the skin.
Line a baking tray with baking paper, then lay the pumpkin slices on the tray.
Drizzle a generous amount of EVOO over the pumpkin. Strip the rosemary leaves from the sprig and scatter them on top. Then add a sprinkle of salt and freshly ground black pepper.
Add two garlic cloves to the tray. Roast everything in the oven until the pumpkin is soft, checking after 20 minutes to make sure it’s not burning and turn to roast equally on both sides.
Once roasted, transfer all the pumpkin, rosemary, and garlic into an immersion blender. Pour in a generous amount of EVOO and blend until creamy. If it's hard to blend, add more EVOO. Set aside.
Bring a large pot of water to a boil then add 1 tablespoon of rock salt and allow it to dissolve. Add in the pasta of choice and cook according to the package instructions, stirring occasionally.
Scoop up a mug full of pasta water (once there is minimal cooking time left) and add some to the blender with the pumpkin cream, sprinkle in pecorino, and blend again. If it’s too thick, add more pasta water.
Use a spoon to mix further until you get a smooth, creamy consistency.
In a large pan, heat a bit of EVOO and add a splash of pasta water along with the pumpkin cream. Swirl some more pasta water into the blender to get all the remaining cream, so nothing is wasted, and add it to the pan. Stir, and add more pasta water if the sauce seems too dry.
Transfer the pasta into the pan and toss to coat the pasta evenly with the sauce. Add pasta water as needed to keep the mixture creamy.
Turn off the heat and sprinkle in some Pecorino cheese and the crushed walnuts, saving a portion for garnish. Toss to ensure all ingredients are well incorporated.