1. Bring a medium saucepan of water with 1/2 tsp salt to a boil. Blanch green beans and carrots for 2 minutes; drain. Set aside.
2. In a 4- to 5-quart heavy pot, cook curry paste over medium heat, stirring constantly for 1 minute. Whisk in coconut milk, chicken broth, fish sauce, and sugar, and simmer briskly until liquid is reduced by about one-third (10-15 minutes).
3. Add sweet potato to pot and simmer until it begins to soften (5 minutes). Add chicken, if using, bring to a simmer, and cook until no longer pink (5 minutes). Add zucchini, blanched vegetables, and tofu (if using). Continue to cook, covered, until zucchini is just tender (3-5 minutes more). Serve.
*To make this dish vegetarian, substitute vegetable broth and soy sauce for the chicken broth and fish sauce.