Turn heat to low and stir brussels sprouts so that they cook evenly. You want them to cook slowly and get the rich color and caramelize on all sides. This should take about 5-10 minutes.
Add brussels sprouts and lay cut side down on pan. Brown the brussels sprouts till they are golden and slightly crisp on the cut side.
Heat large heavy bottom skillet, on medium heat. Add vegetable oil.
Reserve the loose brussels sprouts leaves and cook them if you like alongside the brussels sprout halves.
Wash and trim ends of brussels sprouts. Cut them in half or quarters, depending on their size for even cooking. If you have a mix of very large and small brussels sprouts, make sure to cut them around the same size so that they cook evenly.