Prepare the salmon by checking thoroughly for small bones. You may need to use a tweezer to pull them out if you find any.
Place a large roasting pan over two burners on your stove top.
Cut one of the lemons into slices and put them in the roasting pan. Juice the second lemon and add the juice to the pan.
Cut the leeks in half, clean them carefully and place them in the pan
Cut the fennel in half and slice it. Add this to the pan.
Clean the celery and add it along with some a good handful of thyme sprigs.
Place the salmon on top of the vegetables in the pan and just cover with cold water. You may need to cut the smaller end off the salmon to make it fit.
Season the water liberally with salt.
Turn the burners to medium heat. Watch the water temperature carefully. You don’t want it to go over 170 degrees. Carefully stir the water from time to time to distribute the heat.
After about 15 minutes test the salmon with an instant read thermometer. The salmon is done when it reaches 120 degrees in its thickest part.
Carefully remove the salmon from the water bath and place it on your serving platter.
Let it cool, then drain any water which has pooled around it, cover and refrigerate until well chilled.
For the Sauce
Slice the jalapeno and remove the white pith and seeds
Place all of the ingredients, except the oil in a blender or the small bowl of a food processor.
Pulse it a few times until the herbs are chopped and everything is incorporated.
With the motor running, slowly pour in the olive oil.
Remove the sauce to a bowl or container and refrigerate until you are ready to serve it.