Start by peeling your apples, then coring and cutting them into small dice. This ensures they'll cook down nicely and fit into your pierogi shells.
4 large apples
In a medium skillet, melt the butter over medium heat. Add the diced apples, sugar, cinnamon, nutmeg, and a pinch of salt. Cook, stirring occasionally, until the apples are tender but not mushy, about 5-7 minutes.
1 teaspoon ground cinnamon, 1/4 teaspoon ground nutmeg, A pinch of salt
Stir in the lemon juice and vanilla extract, cooking for another minute. Then, remove the pan from the heat and let the filling cool.
1 tablespoon lemon juice, 1/2 teaspoon vanilla extract
Taste and Adjust: Once your filling has cooled slightly, give it a taste. Adjust the sugar if needed.
In a large bowl, mix the flour and salt. Make a well in the center and add the egg, oil, and water. Mix until the dough starts to come together, then knead it on a floured surface for about 5 minutes. Let it rest for at least 20 minutes under a clean kitchen towel.
1/4 cup granulated sugar, 2 cups all-purpose flour, 1/2 cup water, 1 large egg, 1 tablespoon vegetable oil, 1/2 teaspoon salt
Roll the dough on a floured surface until it's about 1/8 inch thick. Use a round cutter to cut circles for your pierogies.
Fill and Shape: Place a small spoonful of the apple filling in the center of each dough circle. Fold the dough over the filling to create a half-moon shape. Press the edges together firmly to seal.
Bring a large pot of salted water to a boil. Cook the pierogies in batches, being careful not to overcrowd the pot. They're done when they float to the surface, about 3-4 minutes. Optionally, sauté the boiled pierogies in butter until golden brown.
2 tablespoons unsalted butter