Make the brownie layer: Oil a 12-by-17-inch rimmed baking sheet and line with parchment paper. Melt the butter and chopped chocolate in a small saucepan, stirring, until smooth. Mix the granulated sugar, cocoa powder and vanilla in a stand mixer fitted with the paddle attachment. Add the butter-chocolate mixture and mix on medium speed until combined. Mix in the eggs until combined. Mix in the flour and salt until partially combined, then scrape down the bowl and continue mixing until just combined. Spread the batter in the prepared pan; set aside.
Make the pecan filling: Bring the butter, brown sugar and heavy cream to a boil in a medium saucepan over medium-high heat, stirring occasionally. Add the pecans and stir until well coated. Remove from the heat, let cool briefly and spoon on top of the raw brownie batter in the pan; set aside.
Make the cookie layer: Oil another 12-by-17-inch rimmed baking sheet and line with parchment paper. Wipe out the mixer bowl; add the butter and both sugars and beat until smooth. Add the egg and vanilla and mix until combined, scraping the bowl with a rubber spatula halfway through. Add the flour, corn syrup, cocoa powder, baking powder, baking soda and salt and mix until smooth. Mix in the food coloring and vinegar. Stir in the white chocolate chips. Spread the cookie dough in an even layer in the prepared pan. Freeze until firm, about 30 minutes.
Preheat the oven to 335 degrees F. Once the cookie dough is firm, flip it on top of the pecan-topped brownie layer. Discard the parchment paper, then press down gently to bond the layers together. Put the empty baking sheet upside down on top of the cookie layer to act as a lid and transfer to the oven. Bake 30 minutes, then remove the top baking sheet. Continue baking until a knife inserted into the center comes out clean, 20 to 45 more minutes.