Preheat your oven to 375°F. Line your muffin pan with paper baking cups. This recipe makes exactly 12 muffins, so don't skimp on the liners.
In a medium bowl, whisk together the 1 3/4 cups flour, 1 tablespoon pumpkin spice, 1 teaspoon baking soda, and 1/2 teaspoon salt. Set aside.
In a large bowl, whisk together the pumpkin puree, 1 cup granulated sugar, and 1/2 cup packed brown sugar. Beat in the 2 eggs, 1/2 cup vegetable oil, and 1 tablespoon vanilla extract until the mixture is smooth and well combined. The color will turn a shade darker, and the smell of vanilla and pumpkin will fill your kitchen.
Slowly add the dry ingredients to the wet ingredients, mixing with a spatula or whisk just until no streaks of flour remain. Do not overmix — a few tiny lumps are perfectly fine and will ensure a tender crumb.
In a separate medium bowl, beat the room-temperature cream cheese until completely smooth and fluffy. Add the 1/4 cup granulated sugar, 1 egg yolk, and 1/2 teaspoon vanilla extract, beating until the mixture is well combined and creamy. The texture should be thick, luscious, and spreadable, like a very soft cheesecake batter.
Divide the pumpkin batter evenly among the 12 muffin cups, filling each about 3/4 full. Drop about 1 tablespoon of the cream cheese mixture on top of each muffin. Use a toothpick to gently swirl the filling into the batter — figure-eight motions working from the center out work beautifully. Don't dig deep; just a few gentle passes are all it needs. It will look messy now, but trust the process.
Bake for 18 to 20 minutes, until the edges are golden and a toothpick inserted into the pumpkin part of a muffin comes out with just a few moist crumbs. Let them cool in the pan for 10 minutes before transferring to a wire rack to cool completely, or serve warm.