In a large bowl, whisk together the gluten free flour blend, tapioca starch, instant yeast, granulated sugar, xanthan gum, and salt. Add the warm milk, eggs, melted butter, and apple cider vinegar. Mix with a spatula or hand mixer until a soft, sticky dough forms. Cover with plastic wrap and let rise in a warm place for 1 hour.
Grease a bundt pan generously with butter or nonstick spray. In a medium bowl, combine the sugar and cinnamon for the coating.
Scoop tablespoon-sized pieces of dough and roll into balls with lightly oiled hands. Dip each ball into the melted butter, then roll in the cinnamon sugar mixture until coated. Place the coated balls into the prepared bundt pan, layering them evenly.
Cover the pan with plastic wrap and let the dough balls rise for 30 minutes until slightly puffy. Preheat the oven to 350 degrees F during this time.
While the dough rises, make the caramel glaze. Combine the butter, brown sugar, heavy cream, vanilla, and a pinch of salt in a small saucepan over medium heat. Stir until the butter melts and the sugar dissolves, then simmer for 2 minutes. Pour the glaze evenly over the dough balls.
Bake for 30 to 35 minutes until the top is golden brown and the monkey bread sounds hollow when tapped. Let cool in the pan for 5 minutes.
Place a serving plate upside down on top of the bundt pan, then carefully invert the monkey bread onto the plate. Serve warm and pull apart.