Preheat the oven to 450°F. Line a sheet tray with foil or parchment. Place the trout on the prepared pan and season with salt and pepper. Bake until the fish is firm to the touch and flakes easily when pierced with a fork, 5 to 7 minutes.
To prep the oranges, cut off the tops and bottoms, then trim away the white pith and peel, starting from the top and following the curve of the fruit. Slice the oranges into rounds. In a bowl, toss together the oranges, beets, farro, a drizzle of olive oil, and a pinch of salt.
When the fish is ready, transfer it to plates. Spoon the beets and oranges over the fish and onto the plate, along with the juices. Drizzle the almond salsa verde over the top. Serve warm, with a tossed salad on the side.