Make your Gorgonzola potato pancakes: In a large mixing bowl, combine potatoes, egg, flour, half of the chives, half of the crumbled Gorgonzola and the shredded cheese. Sprinkle in salt and pepper and mix.
In a large skillet, add oil and heat pan to medium heat. Scoop potato mixture into skillet, cook on each side for 4 minutes, flipping, pressing down and flipping once more. Remove from heat.
In the same skillet, add butter and slices of bread. Reduce heat to low and build your sandwich: Add a layer of caramelized onions and sliced cheese. Sprinkle on the remaining Gorgonzola, and top with potato pancakes and chives. Once cheese is melty and bread is golden, combine slices and serve the sandwich hot. Enjoy!