Brush the inside of a large soufflé (32 ounce) with 1 1/2 tablespoons of softened butter all the way to the top of the ramekin. Sprinkle the buttered surface evenly with bread crumbs all the way to the top. (or break it up into different sized ramekins as needed)
Preheat the oven to 375F. In a large saucepan over medium heat, sauté the shallots and garlic in the remaining butter until they turn translucent and tender. Add the crushed red chilies if using and continue to cook for another 2 minutes. Add the flour to the shallots and garlic. Cook the flour, whisking constantly, for 30 seconds. Add the milk to the flour and cook, still whisking constantly, for about 4 minutes, until the mixture thickens. Add the potatoes and cheese and mix until the cheese is melted through about 3 minutes.
Whisk ½ cup of the hot potato mixture into the egg yolks, and then add the egg yolk mixture back into the hot potatoes, stirring to completely incorporate. Stir in the chives.
Beat the egg whites on high speed until stiff but still moist and shiny peaks form. Stir one-third of the egg whites into the potatoes, and then fold the remaining egg whites into the mixture.
Spoon it into the prepared dish and bake for 30 minutes, until the potato soufflé is puffed up and golden brown (the inside may still be creamy, but that is good!). Serve immediately!