Heat 2 teaspoons of oil in a large skillet over medium-high heat. Add the chicken and cook for 5-6 minutes, stirring occasionally, until mostly cooked. Remove and set aside.
Add the remaining oil to the skillet. Sauté the onion and bell pepper for 5 minutes, then add the garlic and cook for 1 minute.
Return the chicken to the skillet. Stir in the tomatoes, coconut milk, chickpeas, cauliflower, curry powder, turmeric, ginger, salt, and pepper. Bring to a boil, then reduce heat, cover, and simmer for 10 minutes. Stir in the spinach and let it wilt for 2-3 minutes.
Serve over rice with cilantro and lime wedges, if desired.