For better flavor go with cooked - at least till nicely softened. For sweeter, denser flavor allow some or all of the onion to brown at least to a light golden.
Add the onion just before the sausage finishes browning.
For color interest and a little sweetness I add a couple tbls very finely minced red bell pepper. Optional.
I make a pound-quart mix when I make it, i.e., for 1 pound of bulk sausage I use 1 quart of milk. Brown the sausage breaking it up well with a fork as it cooks. Add the onion (I use about .5-.75 cup, very finely chopped) and allow to soften well - or brown, your choice. If using, add the red bell during the last minute or two of the onion cooking. If you must, drain the excess fat. (I never do.)
Slowly whisk in 6-8 tbls of flour. Keep stirring the flour as you allow it to cook - a good 2, 3, 4 minutes - till its aroma is toasty. Very slowly at the beginning add the milk, whisking very well as you go, then you can increase the speed as it combines well with the flour and meat. Add a few dashes of Worcestershire and some salt and pepper Bring to a simmer, cook several minutes. Reduce if you want it thicker. Taste, adjust salt and pepper; serve.
