Cut the bones up to fit into a large pot. Add the heads, the bay leaves and all the chopped vegetables. Cover with water by one inch. Set over medium-high heat and bring just barely to a simmer. This should take a solid 15 minutes or so. Let the stock steep at the steaming point, not even simmering, for another 15 to 30 minutes, no more.
Turn off the heat. Set a fine-mesh strainer over a large bowl. Ladle the stock through this to strain out debris, but keeping the fat. You can line the strainer with a paper towel to remove most of the fat, but it will clog repeatedly and you will need to replace the paper towel.
Clean out the stockpot and discard the solids. Pour the broth back into the pot and set the heat to medium. Add all the dried kelp. Bring this just to a simmer, taking about 30 minutes to get there. The moment it simmers, turn off the heat and remove the kelp. Add salt to taste -- it might not need any because the kelp is salty -- and serve.
Notes
I mostly use king salmon bones and heads, but any salmon or trout will work, as will char.
Keys to Success
When you add heads and bones, make sure there are no gills. Gills will make a stock bitter and cloudy.
Don't boil the stock. It will be fishy if you do. Just a bare simmer or even just steaming is what you want.
Don't cook the stock too long, or it will be fishy. This is why you pack the pot with ingredients and just barely cover, so you get a lot of flavor in a short time.
You can skip the whole kombu step, and you can also do it the following day. It really makes the stock better though.
Try to use your stock within a few days. It's much nicer then. It will get fishy as it ages.