In a medium-sized pot, boil butternut squash cubes until fork-tender. Drain and puree squash in blender.
In the same pot over medium heat, cook onion in butter until translucent. Add onions to blender and puree with squash until smooth.
Add about 1/4 cup of the mixture back into the pot, still on medium heat. Whisk in paprika, chili powder, garlic powder, onion powder, and salt. Add cayenne powder if desired.
Deglaze the pot with a splash of soy milk, then whisk in 1 tbsp flour to create the roux. Whisk until the flour is incorporated into the mixture, whisk in the remaining soy milk and squash mixture. Continue cooking until the sauce has thickened, whisking continuously.
Add in the nutritional yeast and daiya cheese shreds and whisk until cheese has melted and everything is incorporated. Remove from heat and set aside.