Preheat the oven to 350°F (175°C). Grease and flour a 9-inch (23 cm) springform pan.
In a large bowl, combine 2 cups (250 grams) of the flour, 1/2 cup (100 grams) of the sugar, baking powder, and salt.
Add 3/4 cup (170 grams) of the cold butter cubes to the flour mixture. Using your fingers or a pastry cutter, rub the butter into the flour until the mixture resembles coarse crumbs.
Add the egg and mix until the dough comes together. If the dough is too crumbly, add 1-2 tablespoons of cold water.
Divide the dough into two portions: about two-thirds for the base and one-third for the topping. Wrap the topping portion in plastic wrap and refrigerate.
Press the larger portion of dough evenly into the bottom and about 1 inch up the sides of the prepared springform pan.
In a separate bowl, toss the sliced apples with lemon juice, 1/4 cup (50 grams) sugar, 1 teaspoon cinnamon, and nutmeg until well coated.
Spread the apple mixture evenly over the dough base in the pan.
Remove the chilled topping dough from the refrigerator. Grate it over the apples using a coarse grater to create a crumbly streusel topping.
Dot the remaining 1/4 cup (55 grams) butter (cut into small pieces) evenly over the streusel topping.
Bake the cake in the preheated oven for 55 to 60 minutes, or until the topping is golden brown and the apples are tender.
Remove the cake from the oven and allow it to cool completely in the pan on a wire rack before removing the springform ring.
Slice and serve the Polish apple cake plain or with a dusting of powdered sugar or a dollop of whipped cream if desired.