Preheat the oven to 350 degrees . Butter a deep (at least 2 inches) 9-inch round cake pan. In a medium saucepan, melt 4 tablespoons of the butter. Add the brown sugar and maple syrup and stir over medium heat until the sugar bubbles. Remove the pan from the heat and stir in the apples, nuts, lemon juice, cardamom and a pinch of salt. Spread the mixture over the bottom of the prepared cake pan.
In a medium bowl, whisk together the flour, baking powder and 1/4 teaspoon of salt. Set aside. In a mixer fitted with a paddle attachment, beat the remaining 8 tablespoons of butter just until smooth. Add the granulated sugar and beat on medium speed until light and fluffy, about 2 minutes. Add the eggs, 1 at a time, and beat until incorporated. Mix in the vanilla. Reduce the mixer speed to low and add the flour mixture to the batter in 3 parts alternating with the buttermilk in 3 parts. Mix until the ingredients are just combined. Turn off the mixer and finish mixing the batter by hand with a large rubber spatula until the flour is fully incorporated.
Drop the batter by spoonfuls onto the apple-nut mixture and spread to fill the pan. Don'tworry if the layer of batter is uneven; it will even out during baking.
Slide the cake into the oven and bake until golden and the center springs back when lightly touched, about 35 minutes. Let the cake cool on a wire rack for about 5 minutes, then flip the pan over onto a serving plate. Let the cake sit upside down for a moment, then pull the pan away. Serve warm or at room temperature.