Preheat the oven to 350 degrees F (175 degrees C). Grease an 8 1/2-inch round baking pan.

Mix flour, sugar, baking powder, and cardamom together in a bowl. Add 3/4 cup plus 1 1/2 tablespoons milk, melted butter, and vanilla extract; stir until combined.

Pour batter into the greased baking pan. Arrange apple slices over the top. Press them firmly into the batter, but make sure the slices are still visible. Sprinkle pearl sugar and cinnamon over the apples.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 40 minutes.