Preheat your oven to 375℉ (or 190℃) and line 1 (and half of another) standard muffin pan with liners.
Next, in a large mixing bowl, measure and add flour, pumpkin spice, ground ginger, baking soda and fine sea salt. Whisk to combine.
In a separate bowl, measure and add eggs, sugar, pumpkin puree, olive oil, unsweetened apple sauce and pure vanilla extract. Whisk to combine.
Pour the pumpkin mixture into the bowl with the dry. Switch to a spatula and mix until the flour is incorporated. Set this off to the side for a moment.
PREPARE THE CHEESECAKE FILLING:
In a mixing bowl, combine softened cream cheese, egg and vanilla extract. If you desire more of a sweetened cheesecake filling, mix in 1 tablespoon granulated sugar.
In your prepared pan, measure and drop 2 tablespoons of the pumpkin batter into each of the paper liners. Tap on the countertop to settle it a bit.
Divide the cheesecake filling (about 1 tablespoon per muffin) top the pumpkin batter.
Lastly, top with 2 more tablespoons of the pumpkin batter.
Slip the pans into your oven and bake for 18 to 22 minutes. Rotate the pans halfway through baking. The muffins are done when a tester is inserted and only a few crumbs come out attached.