Adjust oven rack to middle position and heat oven to 450 degrees. Toss brussels sprouts, potatoes, shallots, carrots, garlic, 1 tbls oil, thyme, rosemary, sugar, 3/4 tsps salt and 1/4 tsps pepper together in bowl.
Spread vegetables into single layer on rimmed baking sheet, arranging brussels sprouts cut side down in center of pan. Roast until vegetables are tender and golden brown, 30 to 35 minutes, rotating pan halfway through cooking.
Whisk parsley, capers, lemon juice, and remaining 2 tbls oil together in large bowl. Add roasted vegetables, toss to combine, and season with salt and pepper to taste.