Other moms cook sausage in one frying pan while cooking eggs in another. I would burn everything. All the sausage you have ever eaten at home came from a hot oven.
Breakfast sausage links, usually labeled "original" or "old-fashioned" rather than "maple" or other odd things
Preheat oven to 400.
Put sausage in a glass pan in one layer.
Put pan in oven.
Leave for 15 minutes.
Then you can either cut it open to see if it's brown all the way through, or leave it in until it looks very dark the way Mom does it and you know for sure it's brown before you take it out.
Cooking it to almost black would have worrisome implications if you ate sausage more than once every three months. Used very sparingly, I think it's great.
If you switch the oven to broil after cooking this way, so you can do toast, expect the toast to get done extra fast because the oven is extra hot.
Look up how to cook bacon in the oven. You need a cookie sheet and aluminum foil, and it's quicker than sausage. I don't have a method yet, but I've done it, and it's almost as good as pan-cooked and much easier to do it for six or more people.