Have all ingredients at room temperature, but if your cream cheese is still cold, microwave it for 15-20 seconds or so to soften it.
Beat the softened cream cheese with an electric mixer on medium speed until blended and smooth.
Add Greek yogurt and mix to incorporate.
Add sugar and spice; beat until incorporated.
Add vanilla, beat until incorporated.
Lightly beat one egg, add to batter and beat briefly just to combine. Repeat with remaining eggs, one at a time.
Add butternut squash; beat just until incorporated and smooth.
Spray baking pan with cooking spray. Pour batter into pan.
Bake in middle of oven at 325 degrees for about 35 to 40 minutes, or until center is almost set (the center should jiggle slightly when pan is gently shaken). If you are using a springform pan, adjust baking time accordingly.
Remove from oven and cool on a rack. When completely cool, chill for at least a few hours (or place in freezer for about 30-40 minutes).
NOTE: I tried adding a couple tablespoons of almond milk to the mashed butternut squash and mixing in well. I think the cake came out even a bit lighter in texture. If you try this, be careful not to use too much almond milk because it would make the butternut too runny.