Meanwhile, toast caraway seeds in a small saucepan over medium-low heat until fragrant, about 2 minutes. Transfer to a medium bowl. Add 1 1/2 teaspoons oil, carrot and shallot to the pan. Cook, stirring occasionally, until very soft, 5 to 7 minutes. Stir in vinegar and remove from heat. Stir into the caraway seeds and slowly whisk in the remaining 3 tablespoons oil, 1/8 teaspoon salt and 1/4 teaspoon pepper.