Mix water, sugar, and butter in a pan over medium heat. Bring to a boil, then remove from heat.
Add vanilla and cinnamon, then gradually mix in flour with a wooden spoon, ensuring no pockets of flour remain. Stir until the lumpy dough smooths out; Continue until it starts to ball up and pulls away from the pan's sides.
Add eggs one at a time; the dough will appear wet and gloopy until each egg is fully incorporated.
Peel and chop the apples. Stir the apples in the beignet batter.
Preheat 3 inches of vegetable or peanut oil in a deep fryer or pan over medium-high heat to 350 degrees. Test the temperature by placing a small dough piece in the hot oil; it should bubble and start cooking.
Carefully drop your apple batter by heaping teaspoons into the hot oil. Fry for 5 minutes (about 2 1/2 minutes on ech side) until gech side is golden brown.
Remove the beignets from the oil with a slotted spoon and place on a cooling rack or paper towels. Sprinkle with liberlly with powdered sugar.