Using a stand mixer with a paddle attachment, combine the brie and shredded cocoa cardona cheese until nicely incorporated.
Divide into 4 equal portions and, using parchment paper, flatten out to fit atop a piece of the bread.
Assemble the sandwiches by layering bread with the flattened cheese mix, a scattering of bittersweet chocolate chips, a layer of sliced bananas, and a piece of the country white bread.
Make 4 equal sandwiches.
In a large heavy-bottomed skillet over medium heat, melt half of the butter until foaming and place the sandwiches into griddle.
Allow sandwich to cook for about 1-2 minutes on each side, adding the remaining butter before flipping.
Remove the sandwiches once the bread is lightly crisped on both sides. Place onto a sheet pan with a metal rack and bake in the preheated oven for a few minutes, checking often. Sandwiches are finished baking when the cheese is really melted and gooey.