Preheat the oven to 350 degrees F. Butter and flour a 9 by 13-inch pan.
Place the softened butter in a large bowl or the bowl of an electric mixer, and whisk until it is pale yellow and light. Add the sugar and whisk until the mixture is light and fluffy. Whisk in the cooled chocolate, then add the eggs 1 at a time, whisking after each addition. Whisk in the vanilla and liqueur, sift in the flour, cocoa, and salt and fold them in until combined. Transfer the batter to the prepared baking pan, smoothing it out evenly, and bake in the center of the oven until the brownies have puffed slightly around the edges and are shiny on the surface, about 30 minutes. They will be very moist in the center. Allow the brownies to cool 4 to 6 hours, but overnight is best.
When you are ready to make the baklava, preheat the oven to 375 degrees F.
Brush the fillo sheets with clarified butter and stack them. Cut fillo sheets into 4 (6-inch) squares. Brush one side of the 4 squares with some caramel sauce and sprinkle with half of the chopped pecans. Cut the brownies into 3-inch squares (reserve remaining brownies for another purpose) and place one on each fillo square. Fold fillo sheets around the brownies like an envelope, brush them with clarified butter, and place them seam-side down on a baking sheet. Bake until they are golden brown, about 4 or 5 minutes.
Carefully place them on plate with a scoop of ice cream. Cover in caramel sauce, chocolate sauce, and pecans and enjoy.