Heat the oil in a skillet over medium-high heat. Add the grated carrot and cook, stirring often, until carrots soften, 7 to 8 minutes. Transfer carrots to a paper towel lined plate to drain and cool.
When the carrots are cool mix them together in a bowl with the yogurt, lemon juice, garlic, ¼ tsp salt, and ⅛ tsp pepper. Taste and season with extra salt & pepper if necessary. Sprinkle the dill and caraway seeds on top. Serve with bread.
