Whisk the sauce. In a bowl, combine hot sauce, soy sauce, brown sugar, rice vinegar, ketchup (if using), sesame oil, and red pepper flakes. Taste and adjust sweetness or heat. Set aside.

Prep the chicken. Pat dry and season lightly with salt and pepper. Bite-size pieces cook quickly and stay tender.

Sear the chicken. Heat 1–2 tablespoons oil in a large skillet or Dutch oven over medium-high. Add chicken in a single layer. Cook 4–6 minutes, stirring once or twice, until browned and just cooked through. Transfer to a plate.

Sauté aromatics and veggies. In the same pan, add a splash more oil if needed. Add garlic and ginger; cook 30 seconds until fragrant. Stir in bell pepper, broccoli, and carrots. Cook 3–4 minutes until crisp-tender.

Build the base. Pour in the chicken broth and half of the firecracker sauce. Bring to a lively simmer. This infuses the broth with flavor and seasons the noodles later.

Cook the ramen. Add the ramen bricks to the simmering broth. Cook according to package time (usually 2–3 minutes), loosening with tongs as they soften.

Return the chicken. Add the cooked chicken back to the pot with the remaining sauce. Stir to coat everything in that glossy, spicy mixture.

Thicken (optional). If you like a saucier, cling-to-the-noodle finish, stir in the cornstarch slurry. Simmer 1 minute until slightly thickened.

Finish and brighten. Turn off the heat. Stir in most of the green onions and a squeeze of lime. Taste and adjust with more soy for salt, vinegar or lime for tang, or hot sauce for heat.

Serve. Ladle into bowls. Top with remaining green onions, sesame seeds, and cilantro. Add extra lime wedges on the side.