Butterflying a hot dog or sausage increases the surface area available for the Maillard reaction (all the awesome taste sensations that come from browning and burning. It also decreases cooking time and allows for more even cooking; a thick sausage cooked whole will often be dry on the outside in order to get it fully cooked at the center.
The trick to effective butterflying is to put the open side down on a hot pan (a bit above medium will usually do it) for a minute or two. Do not press down as you’ll lose juices. Flip the sausage or hot dog and lower the heat to a little below medium. You’ll see juices rise to the top like when you cook a burger. Again, do not press down and lose the juices.
Total cooking time should be less than usual. When you take it off, place it flayed side up on a dish and let it sit for 3-5 minutes so any juices soak into the meat and aren’t lost to the plate when cutting. Enjoy the lovely burnt/browned umami!