Preheat oven to 400°. In a medium saucepan over high heat, bring 3½ c. water and a large pinch of salt to a boil. Add farro and reduce heat to medium-low. Simmer, stirring occasionally and adding more water if needed, until farro is tender, about 40 minutes.
Meanwhile, on a baking sheet, toss carrots, leeks, crushed red pepper flakes, and 1 tbsp. oil; season with salt and black pepper.
Roast vegetables until carrots are softened and leeks are dark golden, about 30 minutes. 4. In a large bowl, toss farro, roasted vegetables, radicchio, bell pepper, beans, and tomatoes.
In a small bowl, combine lemon juice, garlic, parsley, thyme, honey, and remaining ¼ c. oil; season with salt and black pepper. Pour dressing over farro mixture and toss to coat. Add arugula and goat cheese and toss again to combine.
