Preheat your oven to 375 degrees F. Line a 12-cup standard muffin tin with paper liners and set it aside.

Make the cream cheese filling. Beat softened cream cheese with a hand mixer on medium speed for about 1 minute until it is smooth with no lumps. Add the powdered sugar and vanilla extract and beat until fully combined. Set the bowl aside at room temperature.

In a large mixing bowl, whisk together the all-purpose flour, white whole wheat flour, baking soda, baking powder, salt, cinnamon, nutmeg, and ginger until everything is evenly distributed through the dry mixture.

In a separate bowl, whisk together the pumpkin puree, granulated sugar, brown sugar, vegetable oil, eggs, and milk until smooth. Take a moment to make sure the brown sugar is fully broken up with no lumps.

Pour the wet pumpkin mixture into the bowl of dry ingredients. Using a rubber spatula, fold everything together with slow, deliberate strokes until the batter just comes together. Stop as soon as you no longer see dry streaks. Overmixing is the main reason whole wheat muffins turn dense.

Divide the batter evenly among the 12 lined muffin cups, filling each about two-thirds full. Spoon about 1 tablespoon of cream cheese filling onto the center of each cup.

Use a toothpick to swirl the cream cheese gently into the top of each muffin. Pull the toothpick through 2 or 3 figure-eight motions so the filling is partially incorporated but still visible as a swirl.

Bake for 21 to 24 minutes. Check doneness by inserting a toothpick into the pumpkin batter portion of the muffin, not directly into the cream cheese swirl. The toothpick should come out with a few moist crumbs and no wet batter. The tops should feel set when lightly pressed.

Cool in the pan for 5 minutes, then move the muffins to a wire rack to finish cooling. The whole wheat flavor mellows as they cool. Refrigerate leftovers because of the cream cheese filling.