Heat apple cider in a small saucepan over high heat. Bring to a boil; reduce heat and simmer, stirring occasionally, until reduced to 1 cup. Let cool.
In a small bowl, combine sugar and 1 tablespoon cinnamon; set aside.
In a large bowl, combine flour, brown sugar, baking powder, salt, baking soda, nutmeg and remaining 1 ½ teaspoons cinnamon.
In a large glass measuring cup or another bowl, whisk together butter, eggs and apple cider. Pour mixture over dry ingredients and stir using a rubber spatula just until moist, cover and place into the refrigerator until chilled.
Divide dough in half. Working on a lightly floured surface, roll dough into ½-inch-thick rounds; cut out rounds with a 2 ½-inch cutter. Heat vegetable oil in a large stockpot or Dutch oven over medium high heat until a deep-fry thermometer registers 375 degrees F.
Working in batches, add donuts to the Dutch oven and cook until evenly golden and crispy, 1 minute per side. Transfer to a paper towel-lined plate for 30 seconds; then roll warm donuts in cinnamon sugar mixture to coat. Serve.