Preheat your oven to 350°F (177°C) and grease a 8X10 baking dish and line with parchment paper, letting the excess hang over the sides.
In an electric stand mixer fitted with the paddle attachment, add the butter, brown sugar and granulated sugar and mix on medium for 4 minutes, or until light and well blended. With the mixer on low, add in the eggs, one at a time, completely mixing the first before adding the second. Take care to scrape down the sides and bottom of the bowl so that everything is incorporated. Add the oil, milk and vanilla and mix for 1 minute more.
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 and mix on low until just combined.