Season fish inside and out with salt and pepper. Pour about 1 tablespoon of oil into a large roasting pan, reserving the rest of the oil. Lay the fish in the pan and holding the sliced side of the lemon half against your palm, squeeze the juice into the inside cavity of the fish. Stuff the inside cavity with shallots, cilantro, and the thyme. Slice the rest of the lemon and lay the slices on the top (outside surface) of the fish and drizzle the rest of the oil on the outside of the fish.
Roast until internal temperature reaches 135 degrees F, about 20 minutes. (There will be some carryover cooking even after you remove fish from oven.)
Let rest and transfer to a platter. Serve family style with whipped potatoes.