Heat a large, heavy bottomed pan over medium-high heat. Add in the butter and olive oil. When it melts, evenly distribute some pinches of salt and cracked pepper around the pan.Add the brussels sprouts to the pan, cut side down in a tight pattern. When all the sprouts are in a single layer, cover the pan and cook for 10 minutes.The brussels sprouts are done when they are fork tender and deliciously browned. Remove them from the heat.In a mixing bowl, add the balsamic and honey. Add in the brussels sprouts and mix gently with a rubber spatula to coat.Serve hot and happy eating!