Heat avocado oil in large skillet over medium high heat. Add ginger and sizzle for 30-60 seconds, then add chicken. Cook, stirring frequently, until chicken is no longer pink, about 5 minutes.
Add onion, bell pepper, and garlic and stir to combine. Allow onion to soften slightly, about 2 minutes. Add carrot, cauliflower, and curry paste and stir well. Add coconut milk and stir until coconut cream has melted. Reduce heat to medium low and cover.
Cook until carrots and and cauliflower are beginning to soften, about 5 minutes. Add squash, lime juice, and fish sauce, stir well. Cook until veggies are soft and and chicken is cooked through, 3-5 minutes.
Serve with lime wedges and garnish with green onion and cilantro if desired.