Butter a 10" cast iron skillet (or 9" pie plate or cake pan). Preheat the oven to 350°F. Use the convection setting if you have one.
In a small bowl whisk 1 egg for egg wash and set it aside. In another small bowl or measuring cup whisk together the other egg, the yolk, 2 oz whole milk and 1 teaspoon vanilla extract.
In the bowl of a stand mixer or in a large mixing bowl whisk together 7 ½ oz all purpose flour, 4 oz granulated sugar, ½ teaspoon baking powder and ¼ teaspoon table salt. With the mixer running, add 4 oz Irish Butter a tablespoon at a time. Continue mixing until the butter is incorporated. With the mixer running, add the combined eggs and milk.
Spread half the batter into the prepared skillet so that the batter comes about 1/2 way up the sides of the pan. On a sheet of parchment paper or wax paper, spread the rest of the batter into a 9" circle. Cover with another sheet of paper then slide it into the freezer while you prepare the apples.
Peel, core and chop 2 each baking apples into 1/2" cubes. Toss the chopped apples with 2 oz granulated sugar and 1 tablespoon lemon juice. Taste the apples and adjust the flavor to your liking. Pour the apples into the pan and smooth them into an even layer.
Remove the parchment wrapped batter from the freezer. Peel back the top layer of parchment then flip it over so the chilled batter is on top of the apples. Peel off the parchment. Tuck the sides of the batter into the pan to seal in the apples. Brush the top of the cake with egg wash, sprinkle generously with granulated sugar.
Bake until the top of the cake is golden brown, the apples are tender and a toothpick or knife inserted into the cake comes out clean. Total baking time is about 40-45 minutes.
Serve slightly warm with whipped cream. The cake keeps at room temperature for 2-3 days.
Notes
If measuring the flour by volume use the “dip & sweep” method. That is, dip the measuring cup into the flour bin, overfill it, then sweep away the excess.