Combine the following marinade ingredients in a large resealable plastic bag: 2 tbsp olive oil, the thinly sliced onions, Scotch bonnet peppers, ginger, garlic, lemon juice, salt and pepper and massage the marinade to make sure these ingredients are well combined. Add the chicken breasts, and then massage the bag again to make sure the chicken is completely covered by the marinade. Leave overnight in your refrigerator.
Heat up 1 tbsp of olive oil in your cast iron pan or skillet on med high heat. Once hot, remove the chicken pieces from the marinade, and brown both sides, approximately 2-3 minutes each side. Set the chicken to the side. PLEASE NOTE: FOR BETTER FLAVOR YOU CAN GRILL THE CHICKEN PIECES ON YOUR CHARCOAL GRILL!
Keep the heat on med high for now and add 1 more tbsp of olive oil. Add the rest of the contents of the bag (the marinade) to your skillet. You are aiming to caramelize the onions which should take around 20 minutes or so. After around 3-5 minutes, you can lower the heat to medium. During this process, stir every so often and keep an eye on the onions. You want them to brown, but not burn. If the mixture is getting too dry, you can add a little more olive oil.
Once the onions are caramelized, return the chicken to the skillet, and add 1 cup of chicken broth. Bring to the boil, and then reduce the heat to medium and simmer for around 10 minutes until the chicken is thoroughly cooked.
Your glorious Chicken Yassa is now ready to serve!