Preheat the oven to 375 degrees . In a medium bowl, combine 1 cup flour and a pinch salt. Using your fingers, work 6 tablespoons butter into the flour to make coarse crumbs. Sprinkle with 2 tablespoons ice water and stir together until a dough forms. (Add up to 1 tablespoon more ice water if necessary, 1 teaspoon at a time.) Transfer to a work surface and knead briefly before patting into a disk. Lightly flour the work surface and roll out the dough to a 10-inch square. Using a sharp knife, cut out four 4- to 5-inch rounds, depending on the diameter of the serving bowls for the potpies. Transfer the rounds to a parchment-paper-lined baking sheet and bake until golden, 12 to 15 minutes. Let cool.
Meanwhile, in a small bowl, whisk together the curry powder and 1/4 teaspoon each salt and pepper; season the chicken on both sides with the mixture. In a large skillet, melt 1 tablespoon butter over medium heat. Add the chicken and cook, turning once, until golden, about 8 minutes. Transfer the chicken to a plate and let cool; reserve the skillet.
In a medium saucepan, bring the chicken broth to a boil. Add the sweet potato, cover and simmer for 3 minutes. Add the cauliflower, cover and cook until crisp-tender, about 5 minutes; stir in the green beans and cook for 1 minute. Strain the broth into a bowl, reserving the vegetables in the saucepan. Shred the chicken into bite-size pieces and add to the vegetables along with any chicken juices.
In the reserved skillet, melt the remaining 1 tablespoon butter over medium heat. Add the onion and cook, stirring, until golden, about 5 minutes. Stir in the remaining 1 1/2 tablespoons flour and cook for 1 minute. Whisk in the warm broth and cook, stirring, until thickened, about 1 minute. Stir in the chicken-vegetable mixture and season with salt and pepper. Divide among 4 serving bowls, top each with a pastry round and serve immediately.