Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper or aluminum foil.
Toss the squash cubes with the olive oil, garlic salt, pepper and pumpkin pie spice. Spread out on the baking sheet and bake for 15 minutes, then toss and bake for 15 more, or until tender when pierced with a fork. Turn the oven down to 350 degrees F.
Add the squash to a food processor along with feta cheese. Blend until completely smooth and pureed. Taste and add salt, if needed. Transfer the puree to an oven safe dish. Bake the dip for about 20 minutes, or until it is warmed through. Remove the dip from the oven and stir. Top with a drizzle of oil, basil, sage and a sprinkling of feta cheese. Serve immediately with pita chips/bread, crackers and/or crusty bread.