Add cream cheese to bowl of stand mixer. Use paddle attachment to beat cream cheese just until smooth.
Add sugar and beat until smooth.
Add sour cream and vanilla and mix until blended well.
In small bowl or 4 cup measuring cup, beat eggs. Add to cream cheese mixture until blended.
Remove 1¼ cups of the cream cheese mixture to small bowl. Add pumpkin puree, cinnamon, and pumpkin pie spice to the small amount. Whisk to blend.
Place baked crust on sheet pan. Pour vanilla cream cheese mixture into cooled, prepared crust.
Pour pumpkin mixture over the top of the vanilla cheesecake mixture.
Run a knife through the cheesecakes to help them blend a little bit where they come together.
Bake for 1 hour to 1 hour 15 minutes. The center will jiggle a little bit and will be a bit sunken.
Turn off oven. Open door for about a minute. Close door and let cheesecake remain in oven for another hour. Remove from oven and let cool completely on wire rack.
Don't worry if you end up with a crack in the center. You will cover it with sour cream or whipped cream. Refrigerate cooled cheesecake for at least 4 hours.
Before serving, whisk together sour cream and brown sugar. Spread over the center of the cheesecake.
Before loosening pan sides, run knife around edge of pan. Then remove pan sides. Dip serrated knife into hot water, wipe with a paper towel, then cut each piece. Store in the refrigerator.