In a large bowl, sift together the cake flour, baking powder, pumpkin pie spice or cinnamon, and salt. Set aside.
In a separate large bowl, whisk together both sugars and the melted butter until combined. Add the egg, egg yolks, and vanilla. Whisk until well combined. Then, whisk in the sweet potato puree and sour cream (or Greek yogurt).
Add the dry ingredients to the wet, and use a wooden spoon or spatula fold to mix until just combined. The dough WILL be sticky, do not be tempted to add more flour. It will firm up in the fridge, and the moisture is what is going to keep the donuts nice and soft in the middle, opposed to them drying out! Cover the bowl with plastic wrap and place in the refrigerator to chill for at least 1 hour. Mine was personally in the refrigerator for 2 hours!
While the dough is in the refrigerator, cut out 14-16 squares of parchment paper and spread them across 2-3 baking sheets. Lightly dust each square of parchment paper with flour. These will be used for the donuts to sit on once shaped and make it easier to transfer the donuts to the oil once ready to fry.
Then, prepare the glaze ahead of time so you are able to dip the donuts while they’re still warm! In a large bowl, whisk together the powdered sugar, honey, milk, browned butter, vanilla and salt until smooth. Set aside.
Once ready to cut the donuts, generously flour your work surface (very generously), along with flouring your hands and a rolling pin.
Dump the dough out onto your work surface, sprinkle the top with more flour, and gently roll/pat it out into a ½-inch thickness. As you are rolling, don’t be afraid to add more flour as needed!
Using a 3” donut cutter, cup, or mason jar lid, cut the donuts out. As you are cutting, dip the cutter into flour as needed to prevent it from sticking. Then, using a smaller 1” cutter or the wide end of a piping tip, cut out little holes in the middle of each donut. Save the little holes for donut holes or add back to the remaining dough to re-roll to cut out more donuts. You should get 14-16 donuts total depending on the size of the cutter you used.
Place the donuts and donut holes onto the prepared parchment paper squares on the baking sheets. Set aside while you heat the oil.
Fill a large, heavy-bottomed pot or Dutch oven with oil, filling ~2” in the pan. Heat on medium-high until it reaches 350F-365F.
Line a wire cooling rack with a thick layer of paper towels.
Once the oil is hot enough, carefully transfer the parchment paper squares with the donuts on them slowly into the hot oil, 2-3 at a time. After 10-15 seconds, pull the parchment paper away from the donuts (it should almost immediately release). Fry the donuts for 1.5-2 minutes on each side (3-4 minutes total), until beautifully golden brown.
Using a slotted spoon, carefully remove the donuts from the oil and to the rack with paper towels. Repeat with the remaining donuts.
While the other donuts are frying, dip the warm donuts into the glaze, making sure to generously coat both sides. Then place onto a cooling rack that’s positioned on top of a baking sheet to let the glaze set.
Serve warm with a cup of coffee.
