Season the chicken thighs with 1/2 teaspoon salt and 1/2 teaspoon pepper.
Heat 2 tablespoons olive oil in a large Dutch oven or soup pot over medium-high heat.
Sear the chicken until golden, about 2 minutes per side; remove to a plate leaving the drippings in the pot.
Add the chopped onion and sliced carrots to the pot and sauté over medium-high heat for about 4 minutes, until beginning to soften.
Stir in the red curry paste, grated ginger, and minced garlic and cook for about 2 minutes until fragrant and the onions are softened.
Return the chicken to the pot. Add 5 cups chicken broth, two 14 oz cans coconut milk, diced tomatoes (if using), soy sauce, fish sauce, brown sugar, bay leaves, and remaining 1/2 teaspoon salt and 1/2 teaspoon pepper.
Cover and bring to a boil, then reduce heat to a gentle simmer and cook, covered, for about 15 minutes or until the chicken is tender enough to shred with two forks.
Remove the chicken and let it cool slightly, then shred with forks.
While the chicken rests, add the chopped red bell pepper, sliced mushrooms, and uncooked basmati rice to the pot and simmer 8–12 minutes, or until the rice is tender; check occasionally.
Remove from heat and discard the bay leaves.
Stir the shredded chicken back into the pot along with minced basil, minced cilantro, 2–3 tablespoons fresh lime juice, and Asian chili sauce or sriracha to taste.
Adjust consistency by adding extra chicken broth or coconut milk if you prefer a less chunky soup, then ladle into bowls and garnish with cilantro, lime, chili peppers, and crushed peanuts as desired.