Preheat oven to 400°F.
Arrange carrots and red onion on a rimmed baking sheet lined with foil. Season with salt and 1/4 tsp. of the black pepper.
Combine 1 Tbsp. balsamic, 1 Tbsp. oil, and mustard in a small bowl; stir with a whisk. Pour marinade over vegetables; toss to coat. Bake for 25 to 30 minutes or until lightly browned and tender, stirring once halfway through.
While vegetables roast, combine farro and broth in a medium saucepan. Bring to a boil over medium-high heat, then reduce heat and simmer gently, stirring occasionally, until farro is tender, 20 to 25 minutes. Drain any excess liquid and transfer to a large bowl. Combine roasted vegetables with cooked farro. Stir in remaining 2 Tbsp. balsamic vinegar and 1 Tbsp. oil.
Combine artichokes, lemon zest and juice, garlic, nuts, parsley, and remaining 1 Tbsp. oil and 1/4 tsp. black pepper in a small bowl.
Divide vegetable and farro mixture evenly among 4 bowls or plates. Top each serving evenly with artichoke gremolata. Garnish with additional parsley, if desired.