Open heart on a work surface. Place one-quarter of the fennel a few inches from the center crease of the heart. Scatter one-quarter of the shallots over it. Place a fish fillet on top, parallel to the crease and season with salt and pepper. Scatter one-quarter of the mushrooms and fennel fronds over top, and, if desired, top with a pat of butter (you'll need a total of 4 tsps.) or a drizzle of olive oil.