
3 cups all-purpose flour, divided
⅓ cup granulated sugar
2 teaspoons quick-rise yeast
1 teaspoon coarse kosher salt
1 teaspoon ground cinnamon
½ cup warm whole milk (120°F to 130°F)
5 tablespoons unsalted butter, softened
2 large eggs, at room temperature; lightly beaten
Vegetable oil, for frying
Cold water
2 tablespoons fresh lemon juice
4 Granny Smith apples
¼ cup unsalted butter
¼ cup granulated sugar
2 teaspoons ground cinnamon
½ teaspoon coarse kosher salt
¼ cup apple cider vinegar
1½ cups powdered sugar
3 tablespoons whole milk
1 teaspoon vanilla extract