Heat your oven to 375 degrees F. Line a 12-cup muffin tin with paper liners or spray the cups well with nonstick cooking spray. Set it aside.

Make the cream cheese filling first so it has time to chill. Beat the softened cream cheese, 3 tablespoons granulated sugar, and 1 teaspoon vanilla together with a hand mixer until completely smooth, about 1 minute. Scrape it into a small bowl, cover, and refrigerate for at least 10 minutes while you make the batter. Cold filling holds its shape during swirling and does not sink into the muffins.

In a large bowl, whisk together the flour, baking soda, baking powder, salt, pumpkin pie spice, and cinnamon until evenly combined. No lumps of spice left.

In a second large bowl, whisk together the pumpkin puree, eggs, brown sugar, oil, milk, and vanilla until the mixture is smooth and the brown sugar is fully dissolved, about 1 minute.

Pour the wet ingredients into the dry ingredients and fold with a rubber spatula just until you see no more dry flour streaks. A few small lumps are fine. Do not overmix or the muffins will be dense and tough.

Divide the batter evenly among the 12 muffin cups, filling each about 2/3 full. Pull the cream cheese filling from the refrigerator. Drop a rounded teaspoon of filling right onto the center of each muffin cup.

Using a toothpick or the tip of a skewer, drag through the cream cheese and batter with 2 or 3 gentle figure-eight motions to create a swirl. Do not over-stir or the cream cheese will disappear into the batter instead of staying visible on top.

Bake on the center rack for 20 to 22 minutes. The cream cheese should look just set and not glossy in the center. Insert a toothpick into the pumpkin part of a muffin, avoiding the cream cheese. It should come out with just a few moist crumbs attached, not wet batter.

Let the muffins cool in the pan for 5 minutes, then transfer them to a wire rack. Eat warm or let them cool completely before storing. The swirl firms up a little more as the muffins cool.