Preheat oven to 350°F. Spray 12-cup bundt pan with nonstick cooking spray (the kind with flour) or grease and flour it.
Whisk flour, baking powder, baking soda, and salt in a medium bowl. Set aside.
Stir melted butter, sugar, and sour cream or Greek yogurt in a large bowl. Stir in eggs, one at a time, then stir in vanilla and white vinegar. Add sparkling cider and dry ingredients and stir just until moistened. Pour into prepared pan.
Place bundt pan on a cookie sheet. Bake for 35-45 minutes, until a toothpick comes out clean.
While the cake is baking, make the glaze. Heat the sugar and sparkling cider in a small saucepan over medium heat until it boils. Boil for 1 minute, then remove from heat.
Cool cake for 15 minutes in the pan. Use a knife to loosen around the edges, then carefully invert the cake onto serving plate. Use a pastry brush to brush the sparkling cider glaze over the top of the cake. Let cool completely.
Make the icing: whisk the melted butter, powdered sugar, and salt. Whisk in the sparking cider, starting with 1 tablespoon and adding more as needed for desired consistency. Frost cake and sprinkle with decorative sprinkles, if desired.
Store loosely covered at room temperature for up to 3 days.