First, general prep: preheat the oven to 350°F. Melt the butter by microwaving in 20-second intervals until it's just melted, and set aside. Line an 8x8 baking dish with parchment paper.
Mix the cinnamon swirl in a small bowl.
Peel the apples and dice into small cubes (about 1 cm). Toss with the granulated sugar and cinnamon in a medium bowl and set aside.
Make the cake batter: In a large bowl, whisk together the flour, sugar, salt, and baking powder.
In a separate bowl, beat the eggs and add the milk and vanilla. Gently pour the liquid into the dry ingredients, whisking together until just combined. Don't overmix! Gently stir in the melted butter, stirring only until just mixed.
Pour half the batter into the cake pan, then add half the apples and half the cinnamon swirl mix. Gently stir a bit (easiest with a knife) to distribute the apples and swirl the cinnamon. Repeat with the rest of the batter, apples, and cinnamon.
Bake for 55-65 minutes, until a toothpick inserted in the middle comes out clean. Let cool completely in the pan.
While the cake cools, stir together the glaze ingredients. Add enough milk to make it runny and smooth without going too liquid.
Drizzle the glaze over the cake when it's either fully cooled or slightly warm if you can't wait!