In a medium-large skillet ( you will need it later to stirring the 400gr of pasta) pour the oil and pumpkin, a pinch of salt, and cook covered on medium low heat for 8-10 minutes, until tender.
Boil water for the pasta.
Blend pumpkin with the Pecorino cheese, add salt and pepper as taste. If needs add some hot water, to make the sauce more fluid. Keep warm
Transfer the pork cheek to the same pan and melt the fat over medium-low heat ( we will need it for stirring the pasta). Wait for the Pork cheek to become crispy. Remove and keep warm.
When water boil add coarse salt and cook the pasta until al-dente. With a strainer transfer the pasta directly in to the skillet with fat and stir well over medium low heat . Add pumpkin, some hot pasta's cooking water (about less than half glass) and stir. Add Pork cheek, stir well and serve immediately with some Pecorino Romano on top.