Peel and core the apples, cut into fourths and then into a small dice. You should have a generous cup and a half of apples. Place the butter in a small skillet, and cook over medium heat until the butter is golden brown. Pour the butter into a small dish and reserve for later. Add the apples to the sauté pan without cleaning or wiping it. There will be little brown flecks from the butter — you want these. Add the lemon juice and cook, stirring occasionally until the apples are soft. Scrape the apples out of the pan onto a plate and let cool.
Make the donuts:
In a large bowl, whisk the flour, baking powder, salt, baking soda and spices. In a medium bowl, whisk the brown sugar and and eggs. Slowly stream in the reserved brown butter, then add the vanilla, sour cream and cider. Toss the cooked and cooled apples in with the dry to coat. Stir the wet ingredients into the dry until a smooth dough forms.
On a lightly floured work surface, press out the dough to 3/4-inch thickness. Cut the dough using a small donut cutter and place on two well-floured baking sheets. (Scraps can be kneaded back together and re-rolled.).
Line two baking sheets with paper towels. Pour oil into a large, deep skillet to a depth of 2-inches. Attach a deep-fry thermometer and heat the oil to 365 degrees F to 370 degrees F. Fry the doughnuts until deep golden brown, about 45 seconds on each side. Using a slotted spoon, transfer to the paper towels to drain.
Make the glaze:
Whisk together the bourbon, honey, lemon juice and powdered sugar. If it is too thick, add more bourbon. If it is too thin, add more sugar.
Dip the freshly fried donuts in the glaze and serve warm!