Preheat your oven to 350F.
Place the fish, skin-side down, on a cutting board or directly on your baking sheet. Make sure all the small pin bones are removed (you can ask your fish monger to do this for you).
Sprinkle generously with kosher salt and pepper on the flesh-side. Take the dill and chop finely. Sprinkle over the fish.
Cut half the lemon into thin slices, about 1/8 inch thick. Take the remaining half, and squeeze the lemon juice onto the fish, being careful to catch any seeds.
Arrange the lemon slices (I like to make it look like scales!) over the top of the fish. This will bake some of the lemon flavor into the fish, but is also a part of the presentation).
Transfer the fish to a baking sheet if not already on one, and place into your preheated oven. Cook for 20-25 minutes.
At 20 minutes, your fish will be 'medium' (very soft, just-cooked flesh). At 25 minutes, the fish should be completely cooked through (firm and flaky texture).
After your preferred cooking time, pull the fish from the oven and let it rest for 5 minutes.
Using a spatula, slide the tip between the skin and flesh, then lift. The flesh should pull away cleanly and easily from the skin.
Slice with a very sharp knife if serving individually (the fish will flake instead of cut if your knife isn't sharp enough), or serve 'family style' on top of the mushrooms.
Garnish with fresh dill sprigs.