Bring a small pot with 2 cups water, farro, and 1/2 tsp. salt to a boil over high heat. Reduce to a simmer, cover, and cook until tender, 25-30 minutes. Drain in a wire-mesh strainer and rinse with cold water until cool. Rinse pot with cold water until cool. Reserve pot. While farro cooks, prepare ingredients.

Trim top off beet, peel, halve, and cut into 1/2" dice. Peel, trim, and cut carrot into 1/4" slices on an angle. Peel and mince shallot.

Place beets and carrots on separate halves of prepared baking sheet. Keep vegetables separate to avoid staining carrots with beet juice. Toss each with 1 tsp. olive oil and 1/4 tsp. salt and spread into a single layer on their half. Toss carrots first to avoid staining with beet juice. Roast until beets and carrots are crisp tender, 18-20 minutes. While vegetables roast, candy walnuts.

Place sugar and 2 Tbsp. water in a small non-stick pan over medium-high heat. Once sugar has dissolved, add walnuts and a pinch of salt. Cook, stirring occasionally, until sugar crystalizes on walnuts, 2-4 minutes. Remove walnuts from pan.

Stir together seasoned rice vinegar, shallot (to taste), 1 Tbsp. olive oil, 1/4 tsp. salt, and a pinch of pepper in reserved pot. Add cooled farro, arugula, and roasted vegetables to pot and toss to combine.

Top salad with walnuts and goat cheese (crumble with your hands if needed). Place a portion on a plate and serve.