Preheat your oven to 375 degrees F. Line a standard 12-cup muffin tin with paper liners or grease each cup well with nonstick spray. Set the pan aside while you make the filling first so it can firm up slightly.

Make the bourbon vanilla cream cheese filling: In a medium bowl, beat the softened cream cheese with a hand mixer or a fork until it is completely smooth with no lumps, about 1 to 2 minutes. Add the powdered sugar, bourbon, and vanilla extract for the filling. Beat again until everything is combined and the mixture looks creamy and holds a soft shape. Place the bowl in the refrigerator while you mix the batter. A cold filling is much easier to drop onto the batter without it sinking in.

Make the pumpkin batter: In a large mixing bowl, whisk together the pumpkin puree, eggs, vegetable oil, granulated sugar, brown sugar, and the 1 teaspoon of vanilla extract for the batter. Whisk until everything is smooth and the mixture looks uniform in color, about 30 seconds.

In a separate large bowl, whisk together the flour, baking soda, baking powder, salt, pumpkin pie spice, and cinnamon. Pour the wet pumpkin mixture into the dry ingredients and fold everything together with a rubber spatula. Stop mixing as soon as you no longer see dry streaks of flour. A few small lumps are fine. Overmixing will make the muffins dense and tough.

Fill each muffin cup about halfway with pumpkin batter, roughly 2 to 2 1/2 tablespoons per cup. Take the cream cheese filling out of the refrigerator and drop a heaping teaspoon of filling right in the center of each cup of batter. Do not spread it or push it down. It will settle as the muffins bake.

Spoon the remaining pumpkin batter over the top of the cream cheese filling in each cup until the cups are about three-quarters full. The batter does not need to completely cover the filling. A small peek of cream cheese showing through the top is perfectly fine and looks nice once baked.

Bake on the center rack for 20 to 22 minutes. The muffins are done when the tops spring back lightly when you press the center and a toothpick inserted into the pumpkin part of the muffin (not the filling) comes out clean or with just a few moist crumbs. The tops should look set and slightly domed, not shiny or wet.

Let the muffins cool in the pan for 5 minutes before transferring them to a wire rack. The cream cheese center will be very hot right out of the oven, so give them at least 15 to 20 minutes before eating. They taste even better once fully cooled and the filling has had time to set back up.