1. 1. Dissolve the active dry yeast in warm milk and let it sit for 5-10 minutes until foamy.

2. 2. In a large bowl, combine the all-purpose flour, sugar, and salt.

3. 3. Add the eggs and vanilla bean paste, then gradually incorporate the yeast mixture.

4. 4. Knead the dough until it becomes smooth and elastic, about 5-7 minutes.

5. 5. Work in the softened butter until the dough is silky and well-combined.

6. 6. Cover the dough and let it rise for 1-2 hours, or until doubled in size.

7. 7. While the dough is rising, prepare the pumpkin cheesecake filling by beating the cream cheese until smooth.

8. 8. Add the pumpkin puree, powdered sugar, vanilla, cinnamon, pumpkin pie spice, and a pinch of salt; mix until well-combined and silky.

9. 9. Refrigerate the filling until ready to assemble the doughnuts.

10. 10. Roll out the brioche dough to about 1/2-inch thickness on a lightly floured surface.

11. 11. Cut out doughnut shapes using a doughnut cutter or round cookie cutter and place them on a baking sheet.

12. 12. Allow the shaped doughnuts to rise for an additional 30-45 minutes before frying.

13. 13. Heat oil in a deep fryer or large pot to 350°F.

14. 14. Carefully drop the doughnuts into the hot oil and fry until golden brown on both sides, about 1-2 minutes per side.

15. 15. Drain the fried doughnuts on paper towels to remove excess oil.

16. 16. While still warm, toss the doughnuts in the pumpkin spice sugar mixture until fully coated.

17. 17. Fill each doughnut with a generous amount of pumpkin cheesecake filling using a piping bag or small spoon.