Warm the milk to 100 to 110°F (slightly warm to the touch) and pour it into the bowl of a stand mixer. Stir in both sugars and yeast. Allow the yeast to foam and bubble up before stirring in the egg and butter.
Combine the spices with the flour. Add about ½ cup of the flour mixture to the milk mixture at a time, stirring with a wooden spoon to form a thick dough. Attach the dough hook and knead until smooth, about 5 minutes. If the dough becomes too sticky, add a tablespoon more of flour at a time. Cover and let rise until doubled, 45 to 60 minutes.
Roll the dough on a floured surface until about ½ inch thick. Cut out donuts with a round cutter, about 3 ½-inches wide. Gently stack the scraps to re-roll and cut. Cut about 12 donuts. Cover with a kitchen towel and let rise until puffy, about 45 minutes.
Toss together the sugar, cinnamon, and ginger in a bowl bigger enough to fit a donut and set aside. Heat 2-3 inches of oil in a dutch oven or cast iron pan to 365°F. When ready, fry 2 to 3 donuts at a time for about 3 minutes each, flipping halfway. Carefully remove the donuts with a slotted spoon and place on a paper towel lined cooling rack. When cool enough to handle, immediately roll in the cinnamon sugar mixture. Repeat with remaining donuts, maintaining the correct temperature of oil (between 360 and 375°F).
When done, poke a chopstick into one side of the donuts. Use the back end of the chopstick to slightly hollow out the center of the donut. Fill a piping bag fitted with a round tip (about ¼ inch wide) with Raspberry Pie Filling. Insert the piping tip into the hole and gently squeeze to fill the donut. Feel the donut expand in the opposite hand as piping and try to overfill them. Donuts are best enjoyed the same day as they are made.