Cook farro to package directions, then place in a bowl to set aside to cool.
Meanwhile, preheat oven to 475 degrees. Line a baking sheet with aluminum foil. Toss sprouts with 2 tbsp. olive oil, salt, and pepper. Spread on sheet and bake for about 10 minutes. Remove from oven and toss again (or shake the pan to move around), place back in oven and cook an additional 5 minutes. Set aside.
While sprouts cook, make the vinaigrette. Mix lemon juice and dijon mustard together. Season with salt and pepper. Add ¼ cup of olive oil while continually whisking until dressing is well blended.
Toss farro, brussels sprouts, vinaigrette, and citrus segments together in a bowl. Drizzle with vinaigrette.