Preheat the oven to 375 degrees F (190 degrees C). Line a baking sheet with parchment.
Cook bacon in a large skillet over medium heat, turning occasionally, until browned and crisp, 5 to 8 minutes. Drain bacon on paper towels. Crumble bacon when cool enough to handle. Pour off grease, reserving 1 tablespoon in the skillet.
Place skillet with bacon grease back over medium-low heat. Whisk eggs, salt, and pepper together in a bowl; pour into skillet. Cook, without stirring, until eggs begin to set on the bottom and around the edges, about 20 seconds. Lift and fold partially cooked eggs so the uncooked portion flows underneath. Continue to cook until fully set but still glossy and moist, 2 to 3 minutes; stir in bacon. Transfer to a plate to cool.
Stir white sugar and 1/2 teaspoon cinnamon together in a small bowl. Split biscuit dough portions in half horizontally to get 16 portions. Roll each out into a 4-inch circle. Sprinkle cinnamon-sugar mixture over each circle. Spoon about 1 1/2 tablespoons egg mixture into the center of each; top each with 1 cheese cube. Carefully wrap edges of dough around filling to enclose and seal. If needed, roll balls with hands to ensure dough is sealed.
Arrange balls, seam side down, on the prepared baking sheet. Brush tops of balls with melted butter.
Bake in the preheated oven until deep golden brown, 15 to 20 minutes. Transfer baking sheet to a wire rack; let cool 15 minutes before serving.
Meanwhile, whisk together confectioner’s sugar, water, and remaining 1/4 teaspoon cinnamon to make a thin glaze. Drizzle over bombs.