Preheat your oven to 375°F (190°C). Line a rimmed baking sheet with parchment paper so the cookies don't stick and are easy to remove after baking.

In a stand mixer or using a hand mixer, combine the eggs and white sugar. Beat the mixture on medium-high speed until it becomes pale yellow and fluffy, which should take about 5 minutes. This helps the cookies rise and gives them a tender texture.

Add the vanilla extract and melted, slightly cooled unsalted butter to the egg and sugar mixture. Mix until everything is fully incorporated and the batter looks smooth.

In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, mixing just until incorporated. The dough will be quite stiff at this point. Be careful not to overmix—the cookies will be more tender this way.

Peel, core, and dice the apples into very small cubes (about 3 cups total) right before adding them to the dough to minimize browning. Gently fold the apple pieces into the batter using a wooden spoon or rubber spatula, making sure they are well distributed.

Using a cookie scoop or heaping tablespoon, drop portions of cookie dough onto the prepared baking sheet, spacing them slightly apart. Bake in the preheated oven for 12-14 minutes, until the edges just begin to brown but the tops remain pale. I usually watch closely near the end—the cookies firm up more as they cool.

After the cookies have cooled on the baking sheet for a few minutes, transfer them to a wire rack and dust with powdered sugar. Store at room temperature in an airtight container for up to 5 days, or freeze for longer storage. For an extra touch, I like to dust a bit more powdered sugar just before serving for a pretty finish.