Combine mango with 3/4 cup water, rice vinegar, garlic, and salt in small saucepan. Add most of the brown sugar, reserving 1 teaspoon. Bring to a boil. Reduce heat to medium-low. Cook for 5 minutes. Add habanero peppers and simmer on low for 2 minutes. Mix 2 tablespoon water with cornstarch; stir slurry into the pan. Cook over medium-high until thick, 3 to 5 minutes. Leave mixture chunky or blend for a smoother texture.

Heat 1 tablespoon oil in a large saucepan over medium-high heat. Add chicken thighs and saute until browned, 5 to 7 minutes; sprinkle jerk seasoning over chicken. Add shallot and garlic; cook and stir until shallot begins to soften, about 3 minutes. Reduce heat to medium. Add cabbage, carrots, and reserved sugar. Cook until cabbage is translucent but still a little crunchy, 3 to 5 minutes. Taste for seasoning. Let mixture cool.

Heat remaining vegetable oil in a pan over medium-high heat. Fry plantains until they start to brown, about 5 minutes. Transfer plantains onto a paper towel and let cool.

Separate and place egg roll wrappers onto your work surface. Mix egg with water for the egg wash.

Lay out one wrapper with a corner pointed toward you. Use a slotted spoon to add some of the chicken and cabbage mixtures across the center. Sprinkle plantain bits on top. Use your finger or a pastry brush to lightly moisten edges of wonton wrappers with egg wash. Fold one corner of the wrapper over the filling onto the opposite corner to form a triangle. Press edges together to seal. Fill and fold remaining egg rolls.

Heat oil in a large saucepan over medium-high heat. Fry egg rolls in batches in the hot oil, turning occasionally, until golden brown, about 5 minutes. Remove from oil and drain on paper towels or rack. Serve with the mango-habanero sauce.