Prepare your workspace by lining a baking sheet with paper towels and setting up a cooling rack on top. This creates the perfect draining station for your fritters.
Mix the dry ingredients in a large bowl by whisking together flour, sugar, baking powder, cinnamon, nutmeg, and salt until well combined.
Combine the wet ingredients in a separate medium bowl, beating eggs, milk, melted butter, and vanilla extract until smooth.
Create the batter by pouring the wet mixture into the dry ingredients, stirring gently just until combined. The batter should be thick but still drop from a spoon.
Fold in the diced apples gently, being careful not to overmix. You want the apple pieces evenly distributed throughout the batter.
Heat your oil in a heavy-bottomed pot to 350°F (175°C), using a candy thermometer to monitor the temperature. The oil should be about 2 inches deep.
Form the fritters by using a ¼ cup measure or ice cream scoop to carefully drop batter into the hot oil, working in batches of 3-4 fritters at a time to avoid overcrowding.
Fry each fritter for about 2-3 minutes per side, flipping once, until they reach a deep golden brown color. Monitor the oil temperature between batches to keep it consistent.
Drain the fritters on your prepared cooling rack, letting excess oil drip away for about 1-2 minutes.
Finish while still warm by dusting with powdered sugar and immediately sprinkling with a small pinch of flaky sea salt before serving.