Melt 2 tablespoons butter in a large skillet over medium heat. Add 3/4 teaspoon caraway seeds and 1 minced garlic clove; cook, stirring, 1 minute. Halve 2 pounds carrots lengthwise and cut into 2-inch pieces; add to the skillet along with 1/2 cup water, 3 tablespoons each brown sugar and cider vinegar, and salt and pepper to taste. Bring to a simmer, cover and cook 15 minutes. Stir in 4 cups shredded red cabbage and season with salt; cook 5 minutes. Remove from the heat and add a squeeze of lemon juice. Transfer to a bowl and top with torn fresh dill and parsley.