Melt butter in a large skillet over medium heat.
Add apples, brown sugar, granulated sugar, cinnamon, nutmeg, and salt. Cook, stirring, until apples soften, 5–7 minutes.
Whisk cornstarch with 2 tbsp water and the lemon juice. Stir into the apples and simmer until thick and glossy, about 1 minute.
Remove from heat. Stir in vanilla, then spread the filling on a plate to cool for 10 minutes.
Lay a wrapper on a board. Spoon 2–3 tbsp filling near one corner, fold sides over, and roll tightly. Seal edges with a dab of water.
Heat oil in a deep pot to 350°F. Fry 3–4 rolls at a time until golden, 2–3 minutes, turning once.
Drain on a rack or paper towels. Rest 5 minutes before serving.