In a medium saucepan, bring water to a boil. Add salt and then carrots and cook until tender, 5 - 6 minutes. Drain the carrots and add back to pan with butter olive oil, butter, pepper, and balsamic vinegars. Cook until a glaze coats the carrots, 5 minutes. Season with salt and pepper. Garnish with parsley. Serve immediately.
Preheat oven to 375. Spray a 9 x 13 baking dish with non-stick pan spray. Prepare vegetables, place them in a large bowl. Whisk together all remaining ingredients except rosemary. Reserve 2 Tbsp of mixture and pour the rest evenly over the vegetables, tossing them together to coat.
Pour into prepared pan and sprinkle with ground pepper and salt. Arrange rosemary sprigs on top. Roast on 375 for 45 - 60 minutes until tender. Top with remaining sauce mixture.