Combine the yeast, water, sugar, milk, salt, shortening, eggs, and vanilla in the bowl of a stand mixer. Pour in 2 cups of the flour and knead on a medium-low speed with a dough hook until well combined. Slowly add in the remaining flour until a nice dough ball forms. Dough should be wet, but should not stick to your fingers or the sides of the bowl.

Spray a large mixing bowl with nonstick cooking spray. Transfer the dough to the bowl, cover with a clean dish towel, and let rise 1 1/2 hours.

Roll the dough out onto a lightly floured surface 1/4 to 1/2-inch thick. Use a drinking glass or round cookie cutter to punch out 12 donuts, re-rolling the dough as necessary to get a dozen donuts and use almost all of the dough. Let rise another 30 minutes.

Meanwhile, heat the shortening in a large pot to about 350 degrees. While the shortening is coming to temperature, make the glaze in a medium-size mixing bowl by whisking together melted butter, powdered sugar, pinch salt, 2 tsp milk, and 1/2 tsp. vanilla extract. Add in water 1 tsp at a time until it is just thin enough to dip something in easily. It shouldn't be runny, but it shouldn't be thick either.

Fry the donuts a few at a time until golden brown, flipping half-way through. It is helpful to do a test donut to ensure that the donut gets cooked through. Transfer the donuts to a wire rack covered with a layer of papertowels. Let cool for 1 to 2 minutes then dip the top of the donut into the glaze and place it back on the wire rack.

Once all of the donuts have been fried, fill a piping bag with the peach pie filling, like you would with frosting. Using a wide-mouth tip, insert the tip into the top of the doughnuts one at a time, squeezing to fill with 1 to 2 tablespoons of peach pie filling per donut.