Preheat the oven to 400 degrees and line a baking sheet with parchment paper.
Add the squash, onion, garlic, olive oil and a pinch of salt & pepper to the baking sheet and toss to coat evenly. Add the thyme and place in the oven for 20 minutes. Toss and cook for another 10 minutes, or until the squash is tender. Remove from the oven and remove the thyme leaves from the stems - discard the stems.
Add everything from the baking sheet to a food processor with the feta, parm, cream cheese and dry seasonings. Blend until smooth and set aside.
Bring the broth to a boil in a stock pot. Add the dry pasta and cook for 8 minutes, stirring frequently. Do not drain the remaining broth.
Pour in the sauce and stir, stir, stir for 5-ish minutes. You want until the pasta to finish cooking and everything to be incorporated. Taste and adjust the seasonings as needed.
Serve hot with sage and more fresh pepper on top.
Video
Notes
The sauce will seem too thin when it is added to the broth and pasta, but just keep stirring and it will thicken up.
If you have leftovers the sauce will thicken in the fridge. Add a little non-dairy milk when reheating the leftovers to thin out the sauce a bit.
I didn't need to add any salt since there was salt in the broth. But depending on the broth you use, you may need to add some at the end.
The sage is purely decoration, so feel free to omit it.