Melt 2 teaspoons coconut oil in a large skillet, preferably nonstick or ceramic, set over medium-high heat.
Add the onion and carrot. Saute, stirring frequently, until the onion is tender, 4 to 5 minutes.
Push the onions and carrots to the perimeter of the skillet and melt the remaining 2 teaspoons coconut oil in the middle of the skillet. Add the curry paste, garlic and ginger to the oil. Saute, stirring the mixture with the onions and carrots for about 3 minutes.
Stir in the cauliflower florets, red bell pepper, coconut milk and broth. Bring to a boil, then reduce heat to a lively simmer. Partially cover the skillet and cook, stirring occasionally, until the cauliflower is almost tender, 5 to 7 minutes.
Add the zucchini and bamboo shoots. Simmer until the zucchini is just tender, 3 to 4 minutes. Take care not to overcook the zucchini.
Stir in the lime juice, cilantro and basil. Serve with jasmine rice.