Preheat oven to 350 degrees F. Grease a 9x13x2-inch baking dish.
In a large bowl, combine the thawed hash browns, onion, and bell peppers. Reserve a 1/2 packed cup of cheese and mix the remaining 1 1/2 cups with the hash brown mixture. Transfer to the baking dish and smooth into an even layer.
In the same bowl, whisk together the eggs, Dijon, hot sauce, half-and-half, salt, and pepper. Pour the egg mixture over the hash brown mixture and gently press down with the back of a spoon to help hash browns absorb the egg.
Cut the rope sausage crosswise into 1/4-inch slices. Lay across the top of the hash browns and gently press into the mixture.
Bake for 45 minutes. Remove and top with reserved cheese. Increase temperature to 400 degrees F and finish baking just until eggs are set and top is slightly brown, about 7 to 10 minutes. Let rest 10 minutes. Sprinkle with chopped chives or parsley if desired, then serve.