In a small bowl, combine curry powder, cumin, salt, and pepper. Place chicken thighs on a plate and rub spice mixture evenly all over thighs.
Heat vegetable oil in a large high-walled skillet over medium-high heat until pan is hot. Add chicken and sear 3-4 minutes on first side, then flip to opposite side. Cook an additional 3-4 minutes until chicken is golden brown. Transfer chicken to a plate and set aside.
In same pan over medium heat, sauté yellow onion, carrots, and sweet pepper in pan drippings until tender. Add garlic, curry paste, and rice and cook an additional 1-2 minutes until rice is slightly toasted.
Pour chicken broth into skillet and bring to a simmer over medium-high heat. Reduce heat to low, nestle chicken into skillet, and cover pan. Allow rice to simmer on low 10-15 minutes until chicken registers 165F, rice is tender, and most of liquid is evaporated.
Stir coconut milk into rice and season with salt and pepper to taste. Top chicken and rice with fresh cilantro and lime wedges and serve immediately while warm. Enjoy!