Filleting trout is a learned skill. Butterflying a fish is even tougher and takes a lot of practice with a sharp knife.
Butterfly trout are best for grilling. Normally the skin is left on the fish, but the ribs and bones are removed. The fish’s body cavity can be opened like a pair of butterfly wings. The tail is also left on the Butterfly filet. The fish is best grilled skin side down. Lay some lemon slices on the grill to keep the filets from sticking to the grate.
Trout and other fish have a lot of fine bones coming from a thick backbone. Pulling the bones out in one piece is a challenge. Even a sharp knife will not get all the bones.
Years ago, I met a guy cleaning a limit of nice trout along the shore of a lake. He was carrying a length of thin-walled steel pipe to filet his fish. The pipe was 18 inches long and ½ inch in diameter. He would first do a quick scaling with his knife. The scaling was on a piece of driftwood. He removed the guts and made a partial cut behind the head. He liked to cook his fish with the head on. Next, he placed the severed backbone into the pipe and pushed the fish down until the pipe was at the tail. His trout were all over 15 inches. When he pulled the fish off the pipe, all the bones were detached from the fish! The flexible bones folded into the pipe and separated smoothly from the meat.
He had a perfectly Butterflied whole trout, ready for the grill.
There is a commercially made Butterfly tool made for this kind of fish cleaning. It’s called the “Wonder Boner”. Instead of using a pipe, they weld a ring perpendicular to the metal rod. The rod screws into a base and comes in several lengths and sizes. Search You Tube for a demonstration. I can see the value of a metal, open ring for bigger and thicker boned fish.
Cooking and serving a perfect Butterfly Fish is often only seen in a fancy restaurant. Try butterflying some fish on your own for a similar presentation.