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, about 15-20 minutes. Let cool completely.
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 1/2 teaspoons cinnamon.
In a large glass measuring cup or another bowl, whisk together butter, eggs and reduced apple cider.
Pour mixture over dry ingredients and stir using a rubber spatula just until moist; cover and place into the refrigerator until chilled, about 1 hour. Divide dough in half.
Working on a lightly floured surface, roll dough into 1/2-inch thick rounds; cut out rounds with a 2 1/2-inch cutter.
Heat vegetable oil in a large stockpot or Dutch oven over medium high heat until a deep-fry thermometer registers 350 to 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.