Consider this a master recipe. You can play with it a lot by changing the fat -- butter, olive oil, sesame oil, lard, duck fat, whatever -- or the salad underneath the fish, and, obviously, by altering the fish you use. I used California halibut, because it is fantastic cooked this way, but almost any fish will work well here, especially freshwater fish. The only sorts of fish I'd avoid butter poaching would be dark, oily ones like mackerel, bluefish, herring or shad. Other oily fish are nice this way, though, like tuna or salmon, sablefish (black cod), or yellowtail.
Salt the fish well and set aside. Slice the squash, cucumber and radishes very thinly into rounds, ideally with a mandoline -- although a knife is fine. Slice the green beans thinly on the diagonal. Toss all the vegetables with a little salt and vinegar and set aside.
Melt the butter in a pot large enough to hold at least 1 piece of fish, and ideally 2, at a time, but small enough so that the pieces of fish are submerged. You can use more butter if you want to, or you can top things off with olive oil. You want the butter to be between 150°F and 170°F. When the butter hits the right temperature, pat the pieces of fish dry with paper towels and submerge in the oil. If the fish sizzles at all, lower the heat. You want the fish to cook gently. Let the fish swim in the butter for about 10 minutes for every 1/2 inch of thickness. One way to do this is to put the submerged fish into a 325°F oven for 15 minutes.
To finish the salad, add a little bit of the melted butter, or use olive oil, and toss well. Put some on everyone's plate. Gently lift out the pieces of fish and lay them on the salad. Grind lots of black pepper over everything. Serve with some good crusty bread.