Chicken With Garlic-Chili-Ginger Sauce

boneless, skinless chicken breast halves, 8 ounces each

Kosher salt

Freshly ground black pepper

5-inch-long piece fresh ginger root, peeled

fat garlic cloves

jalapeño peppers

chicken broth

soy sauce

dark brown sugar

fish sauce

freshly squeezed lime juice, more to taste

Cooked rice, for serving

Sesame oil, for drizzling

bunch roughly chopped basil, for serving

bunch roughly chopped cilantro, for serving

bunch thinly sliced scallions, for serving

European cucumber, thinly sliced, for serving