The key to roasting the egg for the Passover Seder meal is to start by hard-cooking it. If you try to roast a raw egg, it will explode (as I learned years ago when making my very first Seder). Place the egg in a saucepan with enough water to cover it and bring it to a boil. Immediately turn off the heat, cover the pan, and let the egg sit in the hot water until it is well-cooked, about 13 minutes.
Now it's time to roast the egg: you can hold it with tongs above (not in) the flame on your stove, you can place it directly on the rack of a preheated 350 degree oven, or use my favorite method: place it in the toaster oven, where the heating unit is closer to the egg than in the oven, Whichever way you choose, subject the egg to the heat until it just begins to get brown markings and a few cracks.