Melt 4 tablespoons of the butter in a small saucepan over medium heat. Cook until it turns golden brown and smells nutty, then set aside to cool slightly.

Combine the pecans, 1/4 cup granulated sugar, and 2 tablespoons butter in a skillet. Cook over medium heat, stirring, until the sugar melts and coats the nuts. Spread on parchment to cool and harden.

Heat the oven to 350°F. Sprinkle 1/2 cup brown sugar in the bottom of an 8-inch cake pan. Arrange the apple slices over the sugar and drizzle with 2 tablespoons of the browned butter.

In a mixing bowl, whisk together the flour, remaining 1/2 cup granulated sugar, baking powder, and salt. Add the egg, milk, vanilla, and remaining browned butter. Stir until smooth.

Pour the batter over the apples. Bake for 35 minutes, or until a toothpick inserted in the center comes out clean.

Cool the cake in the pan for 10 minutes. Run a knife around the edge, then invert onto a plate. Break the praline into pieces and scatter over the top.