Prep the pan and oven. Heat the oven to 350°F (175°C). Grease an 8-inch square pan or a 9-inch round pan and line the bottom with parchment for easy release.
Prep the apples. Peel (optional), core, and dice the apples into small chunks, about 1/2 inch. You want 2 to 2 1/2 cups of diced apple.
Pat them dry if they’re very juicy.
Mix the wet ingredients. In a medium bowl, whisk the eggs until smooth and slightly frothy. Stir in the sugar until combined.
Add the flour. Sprinkle in the self-rising flour and fold gently with a spatula. The batter will be thick.
If it seems too stiff to fold, add 1 tablespoon milk to loosen. Don’t overmix.
Fold in the apples. Add the diced apples and fold until they’re evenly distributed. The batter should hug the apples.
Pan and smooth. Scrape the mixture into the prepared pan and smooth the top.
If you like, dust with a little cinnamon sugar.
Bake. Bake for 32–40 minutes, or until the top is golden and a toothpick comes out with only a few moist crumbs. If using a deeper pan, add a few more minutes.
Cool. Let the cake cool in the pan for 10 minutes, then lift out to a rack. Cool for at least 20 more minutes before slicing to help it set.
Serve. Enjoy warm or at room temperature.
It’s great plain, with a dusting of powdered sugar, or a scoop of ice cream.