Preheat oven to 375°F (190°C). Line a baking sheet with parchment paper.
In a large bowl, whisk flour, sugar, baking powder, salt, cinnamon, and nutmeg.
In another bowl, whisk milk, eggs, vanilla, and melted butter.
Pour wet ingredients into dry and stir until just combined. Don’t overmix.
Fold in apples and brown sugar gently.
Drop spoonfuls of batter onto baking sheet, spaced 2 inches apart.
Bake 15–18 minutes, until golden and a toothpick comes out clean.
For the glaze, whisk powdered sugar, milk, and vanilla until smooth.
Drizzle glaze over slightly cooled fritters and serve warm.