Slice leek lengthwise, and cut half-moon slices of white and light-green parts. Place in a bowl, fill with water, and set aside.
Preheat a skillet over medium-high heat and add 2 Tbs of olive oil. Add mushrooms and sprinkle with salt and pepper. Let cook undisturbed for one to two minutes to allow bottom side of mushrooms to brown and caramelize, then flip. Continue to sautee until mushrooms are beginning to brown and cooked completely, then remove them from the pan.
Drain leeks. Lower heat slightly, then add 2 Tbs oil to the pan. Add leeks, and sautee, stirring occasionally, until leeks are softened and beginning to brown. Remove from heat.
Carefully cut rind off of cheese, cutting as close to the rind as possible so as not to lose the good stuff. Cut cheese into chunks and place in food processor. Add mushrooms and leeks and pulse until incorporated. The mixture will still be slightly chunky.
Slice bread into two 1/2-inch-thick slices, and spread a thick layer of the cheese mixture on one slice (preferably one without large holes). Top with 2 slices of turkey and close the sandwich. Heat remaining oil in pan, and lightly toast sandwich on both sides. Serve with chips or a salad.