Preheat oven to 375 degrees Fahrenheit. Place stockpot filled with water over stove set to high heat. Add salt and allow to come to a full boil. Prepare a baking sheet with foil or parchment paper and set aside. Once water has come to a boil, add the carrots and let boil for one minute, or until color is vibrant. Transfer to oversized mixing bowl. Repeat with remaining veggies. Once completed, toss veggies with 3 Tbsp olive oil and season liberally with salt & pepper. Place veggies, cut side down on prepared baking sheet. Bake for 30 minutes, or until veggies are golden and slightly soft. Place baked veggies on prepared serving dish, or leave on baking dish. Drizzle with vinaigrette and garnish with chopped parsley. Serve immediately.
Place stick of butter in saucepan over medium-high heat. Allow butter to brown. Take off of heat and strain browned butter through a sieve into a heat safe container. Set aside. In a clean bowl, whisk together Dijon mustard and vinegar. Once butter has slightly cooled, slowly whisk into mixture until fully incorporated. Season with salt and pepper to taste.