Preheat your oven to 350°F (175°C) and prepare a doughnut pan by lightly greasing it.
In a bowl, whisk together the flour, sugar, baking powder, and pumpkin spice until well combined.
In a separate bowl, combine the pumpkin puree, yogurt, egg, and vanilla extract, mixing until smooth.
Slowly add the wet ingredients to the dry ingredients, stirring gently until just combined. Don’t overmix!
Use a piping bag or a spoon to fill the doughnut pan cavities about halfway.
In a bowl, mix cream cheese with a bit of sugar and vanilla until smooth. Use a small spoon to drop a dollop into the center of each doughnut batter cavity.
Bake for 12-15 minutes, or until a toothpick inserted comes out clean. Let them cool for a few minutes before removing them from the pan.
Allow the doughnuts to cool completely. If desired, top with cream cheese frosting or a light sprinkle of powdered sugar.