Mash the ripe banana in a medium saucepan. Add tomato paste, vinegar, 2 tablespoons brown sugar, 2 teaspoons oil, ginger, onion powder, garlic powder, cayenne pepper, salt, allspice, and turmeric. Stir in water to combine.

Bring the mixture to a simmer over medium heat. Reduce heat to low and cook for about 10-15 minutes, stirring occasionally, until thickened. Remove from heat and let cool completely.

If using whole chicken thighs, trim excess fat and cut into 2-inch pieces. If planning to skewer, make pieces roughly the same size for even cooking.

In a large bowl, combine 1/2 cup of the cooled banana ketchup, soy sauce, brown sugar, minced garlic, lemon juice, oil, and black pepper. Mix until sugar is dissolved.

Add chicken pieces to the marinade, ensuring all pieces are well coated. Cover and refrigerate for at least 4 hours, preferably overnight for maximum flavor penetration.

If using wooden skewers, soak them in water for 30 minutes before grilling to prevent burning. Remove chicken from refrigerator 30 minutes before cooking to bring to room temperature.

Preheat grill to medium-high heat (about 375-400°F). Thread chicken onto skewers if desired. Reserve the marinade. Grill chicken for 4-5 minutes per side or until internal temperature reaches 165°F.

Transfer reserved marinade to a small saucepan and bring to a boil. Cook for 2 minutes to kill any bacteria. Use this to baste the chicken during the last few minutes of grilling for extra flavor and glaze.

Transfer grilled chicken to a serving plate. Sprinkle with sliced green onions and toasted sesame seeds. Serve with lemon or lime wedges and any remaining banana ketchup on the side.