In a large pot, combine the sweet potatoes, butter, 1 cup of the brown sugar, ½ cup water, the salt and pepper. Bring the mixture to a boil., stirring to combine ingredients. Reduce the heat to medium-low, cover and cook until the potatoes are tender, about 30 minutes.
Using a slotted spoon, remove the potatoes to a bowl, leaving liquid in pan. Cook the liquid over medium-high heat until the liquid begins to boil., Reduce the heat and cook until liquid becomes a syrupy, 8 to 10 minutes. Remove the pot from heat, return the potatoes to the pot and stir gently to coat with syrup.
Preheat the oven to 425°F.
Make the topping: In a small bowl, mix the brown sugar, cayenne pepper, and salt. Add the pecans and egg white, stir until thoroughly combined.
Transfer the potatoes to a 9-x-13 inch baking dish and spread evenly. Spoon the nut mixture evenly over the potatoes.
Bake the casserole until the potatoes are heated through and the nuts are crisp, 10 to 12 minutes. Serve hot.