Sprinkle 1 tsp (5 mL) of the salt and turmeric over chicken; set aside. In food processor, pureé together garlic, shallots, ginger and 2 tbsp water to make smooth paste; set aside.
Pressing on side of knife, lightly crush lemongrass. Cut into 2-inch long pieces; set aside.
In large Dutch oven, heat oil over medium-high heat. Lightly brown chicken, in batches; set aside. Drain off fat. Reduce heat to medium; cook reserved lemongrass, cardamom, cloves, star anise, cinnamon and mustard seeds, shaking pan, until mustard seeds start to pop, about 1 minute. Stir in garlic mixture, curry paste and sugar; cook, stirring, until fragrant, about 2 minutes.
Stir in stock and coconut milk; bring to simmer. Add chicken and any accumulated juices and remaining salt; reduce heat, cover and simmer until juices run clear when thighs are pierced, about 20 minutes.
Meanwhile, peel and cut each tomato into 8 wedges; remove seeds. Cut eggplants into 2-inch long chunks. Cut long beans into 2-inch long pieces. Add tomatoes, eggplants and beans to pan; bring to boil. Reduce heat, cover and simmer for 5 minutes. Uncover and simmer until eggplants are tender, about 7 minutes.