Place oven rack in top third of oven. If you need to preheat broiler, do so now on High. Mine does not need preheating so I skip this step.
Cut top quarters off of pepper and remove membranes and seeds. Place tops aside, for now. In a baking dish that is safe for the broiler (I recommend a metal one), place peppers on baking dish, laying on their side. Place peppers in oven set to broil on High. Broil for 4 minutes and then flip to other side to broil for another 4 minutes. Remove from oven and turn broiler off. Preheat oven to 450 degrees.
In medium bowl, add cooked couscous, parsley, olive oil, lemon juice, honey, salt, cumin, red pepper, and chopped chicken. Stir together to combine. Add goat cheese and combine. I like the cheese to melt into the mixture so I stir vigorously. But if you want them in chunks, be more gentle as you mix.
Scoop mixture evenly into the 4 peppers. Top with pepper tops and place in preheated oven for 5 minutes, or until tops are cooked and stuffing is heated-through. Serve immediately.