Heat your oven to 400ºF. Line a baking sheet with foil for easy cleanup.
Shred the potato into a mixing bowl and season with salt and pepper. Let sit 5 minutes to help release some liquid. Using your hands, squeeze as much moisture out of the potatoes as you can and transfer them to a second bowl. Stir in the farro and chopped chives.
Heat a heavy skillet over medium heat. Add enough oil so that it comes to a depth of about 1/8-inch. When the oil is hot. Drop handfuls of potatoes into the pan to create 4-inch rounds that are about 1/4 inch thick. Cook for 6 minutes, or until the bottom is golden brown and the top begins to look opaque. Use a spatula to flip, then cook another 4-6 minutes on the second side. Remove from the pan and drain on paper towels.
Place the salmon skin-side down onto a baking sheet. Spread each filet with 1 tablespoon of lemon curd; season with salt and pepper. Bake 12-15 minutes, or until cooked to your liking.
Remove the salmon from the oven and garnish with chopped chives, if desired. Serve with additional lemon curd and the potato-farro rosti.