For the Tom Kha Soup

• 1 cup white onion slices (approximately 1 small white onion)
• 1 tablespoon chopped fresh garlic (approximately 3 large cloves)
• ½ red jalapeño pepper (sliced; or 1–2 Thai chiles, halved)
• 3 slices fresh galangal (or fresh ginger, each slice ¼-inch long)
• 1 stalk lemongrass (pounded with side of knife, cut into 2-inch-long pieces)
• 10 lime leaves (torn, optional)
• 1 tablespoon red Thai curry paste
• 4 cups chicken broth (see Notes)
• 2 13.5-ounce cans full-fat coconut milk (or coconut cream, at room temperature)
• 1 pound chicken breasts (approximately 2 small chicken breasts, cut into bite-sized pieces)
• 8 ounces white mushroom caps (sliced)
• 2 tablespoons brown sugar (or coconut sugar, plus more to taste)
• 2 tablespoons fish sauce (plus more to taste)
• 2 tablespoons fresh lime juice (plus more to taste)