Preheat your oven to 350°F (177°C). Oil a 10-inch (25-cm) cast-iron skillet and make sure you have a rack in the top third of the oven, at least 6 inches (15 cm) from the heat source.
In a large bowl, whisk together the melted butter, brown sugar, oil, granulated sugar, eggs, egg yolk, milk and vanilla and mix until blended. Set aside.
In another medium bowl, whisk together the all-purpose flour, bread flour, baking powder, baking soda and sea salt. Add this to the butter mixture, stirring until barely combined and you still see streaks of flour. Add in the chopped chocolate and peppermint candy (*reserving* several tablespoons of chocolate and candy to sprinkle over the top) and stir until combined and everything is evenly distributed throughout. Add the dough to the skillet, patting it down to smooth any bumps and lumps. Sprinkle the reserved chocolate and candy over the top.
Bake for 22 minutes in the top third of the oven. Wait at least 45 minutes to serve, and I strongly urge you to serve with vanilla ice cream.