1. Heat 1/2 cup coconut milk on medium heat in a large saucepan until bubbly.
2. Add curry paste and stir until fragrant, about 1-2 minutes. Add chicken and toss to coat all pieces. Add turmeric, brown sugar, fish sauce, carrots, 1/2 cup water, and remaining coconut milk. Cover and cook for 10 minutes. Add sugar snap peas, peppers, and zucchini. Toss well. Cover and cook for 2-3 minutes until zucchini is just tender but still firm. Add cherry tomatoes and toss.
3. Transfer to serving dish and garnish with fresh basil, cilantro, and lime wedges, if desired.
If you don’t have a spiralizer, you can also use a peeler to make wide strips, or simply cut into slices.