Combine water, 2 cups brown sugar, and cinnamon sticks together in a saucepan; bring to a boil. Reduce heat and simmer, stirring occasionally, until sugar is dissolved and liquid has reduced into a syrup, about 15 minutes. Remove cinnamon sticks from syrup using a slotted spoon.
Spread butter onto each toasted bread slice. Make 1 layer of buttered bread in a deep casserole dish or oven-proof stockpot. Sprinkle cinnamon, nutmeg, and cloves over bread layer. Sprinkle 1/4 the raisins, 1/4 the peanuts, 1/4 the remaining brown sugar, and 1/4 the Cheddar cheese over bread layer. Repeat layering with remaining ingredients. Pour cinnamon syrup over entire dish; cover with aluminum foil.
Bake in the preheated oven until cooked through, about 30 minutes. Cool for 20 minutes before serving.
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