I consider myself a pretty decent cook, but ever time I try to cook sausage in a pan on the stovetop it doesn't come out right. I'm talking about log sausage here. I find that it is always undercooked in the center when it is seared heavily on the outside, regardless as to how hot I cook it. If I start slow or fast, it still ends up undercooked. When I wait even longer than seems necessary for them to be done they just burst and I lose all the juice from them. What gives?
There isn't a lot of difference from cooking ground beef on the stove to cooking sausage. Perhaps the sausage you're cooking isn't completely defrosted and that's affecting how it is cooking in the pan? Other than that, as long as you have the stove set to around 230-240 degrees, it should cook correctly and fully in about 5-8 minutes. Also, double check that the meat hasn't gone bad as that will affect if it cooks correctly or not.
I use to have that problem with Italian sausage. What I started doing was taking a fork and poking holes through the skin of the sausage and as it cooks turn it over so that its browns evenly. By doing this the heat can penetrate inside. Also you may be just cooking it too fast under a high temperature. Sometimes I make a slight cut in the center to check the inside for any sign of the color pink.
It's common for sausage to deep fried, but that's not how we cook ours. Because we are always after for healthy alternatives, we either boil it in water or steam it to avoid the unwanted calories from the cooking oil. It's quite better that way, I find it better. It may not have that crispness that the you get when fry it, but it still got that tenderness.
You could simply put the sausages in a container that has a covering over it to create more heat convection, or wrap the sausages in aluminum foil and cook it that way - I do the latter a lot when I'm out BBQ-ing at a recreational park or camping. Also did you set the heat med-high on broil, because I set my levels at 350 Fahrenheit degrees and it always cooks my food throughly. Different types of sausage meats and sizes do cook differently, so I do vary my temperature and cooking methods whenever I believe it will effect more beneficially.
I personally almost always cook sausages in an oven if I can. I do this so the whole sausage would be more evenly cooked since the heat would be more evenly distributed as opposed to just coming from the bottom surface of the pan. The best thing about this is that I could just leave it to cook and do other things and by the time I'm done with my tasks, my meal is ready and cooked very well.
I use to have the same problem of not cooking my sausage all the way through as well. One thing that I always did was cut the sausage into little pieces before I cooked it, but that would be if I was making pasta or something alone those lines. Another method that a lot of people use is poking holes into the suasage as it's cooking. That works really good as well, and it's not as tedious as cutting the suasage into little pieces.
It sounds like it may be one of two things (or both) - You're cooking it in a pan that is too thin, and/or you are still cooking it at too high of a temperature. I would suggest using a sturdier pan which will distribute the heat more evenly and avoid hot spots, as well as putting a lid over the pan during the beginning of the cooking process to "steam" the meat first. Towards the end of cooking you can then take the lid off and release the steam and let it brown up on the outside. You can also put a little water in the pan before putting the lid on at the beginning to help add more steam. I"m assuming the sausage isn't froze, considering you mentioned it was in a log form, which you have to mold into patties, and you wouldn't be able to do that if it were still frozen or semi frozen. You should also check to make sure you aren't making the patties too thick. I wouldn't go any thicker than 1/4".
I always grill sausages or put them in the oven. I find that frying them is too difficult. They always end up burnt on the outside and raw on the inside. My advice would be to wrap in foil, bake in the oven for a while theremove the foil for the last 10 minutes of cooking.
If you're shallowing frying sausages you need to remember to pierce them all over. This allows the heat to penetrate through the skin and ensure the whole of the sausage is thoroughly cooked. This sounds like your problem, because I've had the same problem before, but I can't think of what else it could be. Take a fork and pierce the sausage about five times, width way, all the way along the sausage. Try frying again and let us know how you get on! Enjoy your scrummy sausages, nothing better than a fried sausage or three to start your day.