It sounds simple but there are many different methods that claim to be the best. Here are just a few from Derrick Riches’, The Art of Grilling Sausage:
Straight Grilling: Of course, you can place sausages right on the grill and cook them the old-fashioned way. The biggest problem is that people use a high heat and burn the surface before the middle gets cooked. The other problem is that when a sausage cooks it leaks juices that can cause flare-ups and add to the burning problem. To eliminate the burning and the flare-ups you need to keep the fire low. This increases the cooking time but lets the sausage cook gently and hold in its flavor. Some people will tell you to puncture the skin, but this will just let the juices out to start more fires. Keep the sausage casing intact and the heat low.
Boil and Grill: There are two ways to use a boil or simmer and grill method of cooking sausage. One is to parboil them first, partially cooking before they hit the grill. However, if you use plain water you will be pulling flavor out of the sausages. To parboil first, drop sausages into boiling liquid long enough to tighten the skin. Next, place the sausages on a hot grill over a medium low fire and finish cooking. This method gives you juicy sausages and is a sure way to keep the casings from hardening. The other is to grill sausages first over a medium heat, turning frequently until cooked through and then move them to a shallow 'bath' of simmering beer, wine or other seasoned liquid until ready to serve. (Aromatics such as onions, garlic or herbs are great add-ins.)
Split and Grill: This method calls for cutting the sausage lengthwise about 80% of the way through, so you can fold it out and lay it flat. This is a good way to get the inside to cook quickly, although if you are opening up the sausage the juices will drip out. While this may be a leaner way of cooking it tends to dry out the sausages and leaves them lacking in flavor.
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A few notes for grilling the perfect sausage: