Brothy Chicken and Rice with Ginger and Scallions

Name: Brothy Chicken and Rice with Ginger and Scallions
Ingredients: 6 cups reduced-sodium chicken broth; 2 cups water; 2 tablespoons mirin; 1 tablespoon fish sauce; 1 bunch scallions (about 6); 4 ounces shiitake mushrooms, caps thinly sliced, stems reserved; 1 (2-inch) piece fresh ginger, peeled and sliced; 6 garlic cloves, sliced; 1 small bunch basil, plus basil leaves, for serving; 1 large chicken breast (about 12 ounces); 1/2 to 1 red jalapeno, thinly sliced (seeds and ribs removed for less heat, if desired); 1 cup frozen shelled edamame, thawed; 3 ounces (1 cup) julienned jicama; Kosher salt; 2 cups hot cooked brown rice; Lime wedges, serving suggestion