- In a medium saucepan, bring milk, cider, butter, sweetener, and salt to a boil. Immediately add flour and cinnamon and stir vigorously with a wooden spoon on the heat until mixture comes together. Continue stirring until dough is smooth and pulls away from sides of pan. Transfer dough to bowl or stand mixer fitted with the paddle and let cool 10 minutes, stirring occasionally. Add eggs one at a time, stirring or mixing on low speed to completely incorporate each egg before adding the next. Dough should be smooth and shiny. Stir or mix in apples. Set aside.
- In a small saucepan, combine sugar, sweetener, and 1⁄4 cup water. Cook, stirring, over medium-high heat until sugar dissolves. Increase heat to high and cook syrup until deep amber colored, swirling pan as needed to prevent burning. Remove from heat and slowly add cider (be careful–it will splatter). Stir until smooth. If caramel seems runny, simmer until thickened and syrupy. Stir in vanilla and salt. Set aside.
- In a large heavy pot, add oil to a 2” depth. Heat oil to 365°F. Drop tablespoons of dough into oil in batches of 8 and cook until golden all over. Remove with a slotted spoon and drain on paper towels. Repeat with remaining dough.
- To serve, drizzle beignets with caramel sauce and sprinkle with cinnamon.