Preheat your oven to 350°F (175°C). Peel, core, and slice the apples into thin rounds, then set aside.
In a large mixing bowl, whisk together the flour, sugar, ground cardamom, baking powder, and salt until evenly combined.
In a separate bowl, beat the eggs, then add the melted butter and vanilla extract, whisking until smooth.
Pour the wet mixture into the dry ingredients and gently fold with a spatula until just combined. The batter should be slightly thick but pourable.
Lightly grease a 9-inch cake pan and pour half of the batter into the bottom, spreading it evenly.
Arrange a layer of sliced apples over the batter, covering the surface in a decorative pattern if desired.
Pour the remaining batter over the apples, smoothing the top with a spatula to ensure even coverage.
Bake in the preheated oven for 50 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
Once cooled, slice the cake to reveal tender apple layers embedded in the moist crumb, with a fragrant hint of cardamom.
Serve slices of the cake slightly warm or at room temperature, enjoying the combination of soft fruit and cake crust.
