In a bowl, combine the shredded red cabbage and carrots. Squeeze the juice of 1 lime over the mixture. Add 1 tsp olive oil and 3/4 tsp salt. Toss to combine. Taste and add the juice of up to another half lime if desired. Let marinate while you prepare the chicken.

Season the chicken breasts with the remaining 3/4 tsp salt and pepper.

Heat a large nonstick skillet over medium-high heat until hot.

Add the remaining 1 tsp olive oil to the hot skillet. Add the seasoned chicken breasts and cook until golden brown on one side, about 5 minutes.

Flip the chicken breasts. Add the water, peanut butter, Sriracha chili sauce, grated ginger, and grated garlic to the skillet.

Bring the mixture to a boil. Use a spatula to help dissolve the peanut butter into the liquid, creating a sauce.

Reduce the heat to low, cover, and simmer. Flip the chicken occasionally to baste it in the sauce and stir the sauce around. Cook until the chicken is cooked through and the sauce has thickened, about 20 minutes. Cooking time may vary depending on the size of your chicken breasts.

Remove the chicken from the skillet and let it rest for 5 minutes before slicing.

Juice the last lime half into the peanut sauce in the skillet. Stir well to smooth out the sauce.

Divide the marinated cabbage and carrot salad among four plates. Top each with sliced chicken. Spoon the peanut sauce generously over the chicken. Serve with brown rice or veggie rice on the side, if desired.

Garnish with fresh cilantro, if using.