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Step 1
To start, make the filling. Combine the apples, brown sugar, cinnamon, salt, and vanilla in a saucepan over medium heat. Cook until the apples are slightly softened and have released their juices, about 5 minutes. Whisk together the water and cornstarch in a small bowl until a slurry forms. Pour into the apple mixture, stirring constantly, and increase the heat to high. Continue to stir and cook until the mixture thickens and the apples are softened to your desired consistency, about 3-6 more minutes. Stir in the lemon juice. Remove the filling mixture from the heat and set aside to cool.
Step 2
As the filling cools, prepare the dough. Add the flour to a large bowl. Use a dough blender or two knives to cut the butter into the flour until coarse crumbs form, no larger than a pea. In a small, separate bowl, beat together the eggs and the salt. Pour the hot milk (and make sure it's very hot!) slowly into the egg mixture while whisking constantly. It's important to do this slowly or else you'll wind up with scrambled eggs. Add the milk mixture to the flour mixture and stir until well-combined and the dough begins to pull away from the sides of the bowl.
Step 3
Lightly flour a flat surface and turn the dough out on top. Knead the dough until it's smooth, about 2-3 minutes.
Step 4
Cut the dough into 8 (for large) or 12 (for small) equal sized pieces. Roll each piece into a ball, smoothing them out as much as possible. Using a rolling pin, roll the dough out into thin circles.
Step 5
One at a time, fill each dough circle with about 2 tablespoon's worth of the apple filling. Fold the dough circle in half over the filling, and press down on the edges to seal. Fold or crimp the edge, starting at one corner and continuing all the way to the end, to ensure that the pies stay closed while frying.
Step 6
Heat the oil to 350°F in a deep cast iron pan, dutch oven, or wok. If you don't have a candy & oil thermometer, you can tell the oil is ready when bubbles rise to the surface around a wooden spoon handle inserted into the oil.
Step 7
Fry the pies, a couple at a time, until golden brown, about 2-3 minutes per side. You may find that you have to adjust your heat as you go, so keep an eye on how quickly they brown. Carefully remove the pies from the oil using tongs or a slotted spoon and set aside on a cooling rack placed over a baking sheet or paper towels.
Step 8
While the pies cool enough to handle, make the glaze. Place the butter in a medium-sized microwave-safe bowl. Cover the bowl with a paper plate and microwave on high for 3 minutes, and then in 15 second intervals if necessary, until deeply golden.
Step 9
Remove browned butter from microwave and allow to cool slightly. Whisk in the brown sugar, maple syrup, and milk. Microwave again in 30 second intervals, whisking in between, until melted and smooth, about 2 minutes total.
Step 10
Whisk in the vanilla extract and a cup of the powdered sugar. Add additional powdered sugar until the glaze is thick enough to brush onto the fry pies.
Step 11
Brush the glaze onto the tops of the fry pies and let set. Drizzle with remaining glaze, if desired. Allow the glaze to harden slightly and then serve.
Step 12
The pies can be stored on the counter, loosely covered for 3 days. Don't place them in a plastic bag or container, or the glaze will soften.