Bring a large pot of water to a boil. Stir in the rice, cover and boil until tender, about 18 minutes; drain well and keep warm.
Meanwhile, preheat the broiler. Toss the green beans, 1 1/2 tablespoons vegetable oil and the sugar on a rimmed baking sheet. Broil, stirring once, until the beans are tender and charred, about 8 minutes.
Heat the remaining 1 1/2 tablespoons vegetable oil in a large skillet over high heat. Add the turkey and cook, breaking it up with a wooden spoon, until browned, 3 minutes. Add the garlic, pickle and chile paste and cook until the garlic is slightly golden, about 3 minutes.
Whisk the chicken broth, soy sauce, sherry and cornstarch in a bowl. Add the green beans to the skillet with the turkey mixture and cook, stirring, 1 minute. Add the soy sauce mixture and cook, stirring occasionally, until the sauce thickens slightly, about 3 minutes. Serve with the rice.