Heat 2 tablespoons oil in a large Dutch oven over medium-high heat. Add the bok choy and cook 3-4 minutes until charred on the edges. Transfer to a plate.To the same Dutch oven, add 1 tablespoon oil, the mushrooms, shallots, garlic, and ginger. Cook 3-5 minutes, until fragrant. Stir in the broth and bring to a boil over high heat. Add the wontons and cook until they float, 2-3 minutes. Stir in the bok choy, soy sauce, and rice vinegar. Remove from the heat. To make the chili oil: combine everything in a small bowl. Divide the bok choy between bowls, then ladle the soup over. Top each bowl with green onions. Serve the chili oil on the side.