In a large stockpot over medium high heat bring butternut squash, chicken stock, and milk to a boil. Then reduce to simmer cooking until squash is fork tender (about 15 to 20 minutes).
While simmering cook the pasta in another pot according to package instructions.
Remove from heat and add to a blender. Add Greek yogurt and both cheeses. Because the mixture will be hot remove top insert and use a dish towel to vent. Purée until smooth. Add back to original pot.
When pasta is done, drain and place into cheesy squash mixture. Stir until fully incorporated.