In a medium bowl, whisk together the red curry paste, coconut milk, fish sauce, brown sugar, lime juice, minced garlic, and vegetable oil until smooth.

Add the chicken pieces to the marinade, tossing well to ensure every piece is evenly coated. Cover and refrigerate for at least 1 hour, or up to overnight for the best flavor.

Preheat your outdoor grill or an indoor grill pan over medium-high heat and lightly oil the grates to prevent sticking.

Thread the marinated chicken onto the soaked bamboo skewers, alternating with pieces of red bell pepper and red onion.

Place the kebabs on the hot grill and cook for 10 to 12 minutes, turning occasionally, until the chicken is deeply charred on the edges and cooked through to an internal temperature of 165 degrees Fahrenheit.

Transfer the grilled kebabs to a serving platter and garnish with fresh chopped cilantro. Serve immediately with a side of jasmine rice and extra lime wedges.