Add the coconut oil to a large skillet. Add enough vegetable oil to come about a third of the way up the sides of the skillet and heat over medium-high heat until very hot.
Line a baking sheet with paper towels. Mix together the brown sugar, paprika, cayenne and salt in a small bowl and set aside.
Add the plantain slices to the oil in batches and fry until golden brown on the outside, about 5 minutes. Remove from the oil and smash to a chip size with a wooden mallet or rolling pin. Return the plantains to the oil in small batches again so they do not stick together and cook for another 3 minutes. Transfer the chips to the towel-lined baking sheet and top with the seasoning mixture.
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