Cook penne in water with the tablespoon salt until 1 minute short of the package time. Reserve 1 cup pasta water before draining.
Meanwhile, rub chicken with allspice, thyme, paprika, garlic powder, cayenne, brown sugar, chicken salt and pepper. Heat oil in a large skillet and cook for 5 to 7 minutes per side until browned and at least 165°F; transfer to a board to rest.
Cook bell pepper strips in the skillet for 5 to 6 minutes until crisp-tender. Whisk coconut milk, broth and cornstarch, pour into the skillet and simmer gently for 3 minutes.
Slice chicken and return with its juices, add penne and toss for 1 to 2 minutes until the pasta is tender, using a little reserved pasta water if the sauce is too thick.
Stir in lime juice off the heat and serve with the colored pepper strips and sliced chicken evenly distributed.