In a large bowl, whisk together the bread flour, all-purpose flour, granulated sugar, instant yeast, kosher salt, and pumpkin pie spice to evenly distribute the dry ingredients. Set this mixture aside; it will be incorporated with wet ingredients later.

In a small saucepan, heat the whole milk on medium-low heat until lukewarm, about 30 seconds (75-80°F). In the bowl of a stand mixer, beat together the large egg, egg yolk, canned pumpkin, and vanilla extract. Pour the lukewarm milk into the mixer bowl, then add the flour mixture from Step 1. Add the softened, cubed unsalted butter last. Using the dough hook attachment, mix on low speed until the mixture is combined, then increase to medium speed and knead for 10-15 minutes until the dough is elastic and pulls away cleanly from the sides of the bowl. To test readiness, stretch a small piece of dough: if you can see light through it without it tearing, your dough is ready (this is the 'windowpane test').

Transfer the kneaded dough to a large, lightly greased bowl and cover with a tea towel or cling film. Let the dough rise in a warm spot for 45 minutes to 1 hour or until doubled in size. (Alternatively, cover and refrigerate overnight for a slow rise.) While the dough is rising, prepare two baking sheets by lining them with parchment paper and lightly greasing them. Once the dough has risen, punch it down to deflate and turn onto a well-floured work surface. Divide into 14 equal pieces, about 75 grams each, and shape into tight, round balls. Arrange the balls on a prepared baking sheet, leaving a 2-inch gap between each, then gently flatten them slightly. Cover and proof for another 20-30 minutes at room temperature (or about 1 hour if the dough was refrigerated overnight).

While the doughnuts are proofing, prepare the pumpkin cheesecake filling. In a mixing bowl, use a hand or stand mixer fitted with the whisk attachment to beat the pumpkin spice cream cheese spread, sifted powdered sugar, pumpkin pie spice, vanilla extract, and kosher salt until super light and fluffy. Add the heavy cream and continue beating on medium speed until smooth and creamy, about 2 minutes. Cover and refrigerate the filling until ready to use. I like to chill my filling well—it pipes so much more neatly this way.

Heat 2 inches of vegetable oil in a deep fryer or large, heavy pot to 350°F. While the oil is heating, set up a cooling rack over a parchment- or paper towel-lined baking sheet. Fry the proofed dough balls in batches of 2 or 3 for about 2 minutes per side, or until deep golden brown. Use a slotted spoon to transfer each doughnut to the prepared cooling rack to drain and cool. To ensure even browning, avoid overcrowding the pot.

Mix granulated sugar and pumpkin pie spice in a shallow bowl until well blended. While the doughnuts are still a bit warm but not hot, roll them in the pumpkin spice sugar mixture to coat them evenly all over. I like to toss them twice for extra flavor and a beautiful sparkle.

Transfer the chilled cheesecake filling (from Step 4) to a piping bag fitted with a pastry tip. Use a chopstick or small knife to poke a hole in the side or top of each cooled doughnut to create an opening. Gently pipe in the pumpkin cheesecake filling until each doughnut feels slightly heavier but not bursting. Serve immediately or store as desired.