Preheat oven to 425ºF.
Toss carrots and EVOO together on a baking sheet and season with salt and pepper. Roast until tender, about 20 minutes.
Transfer carrots to a food processor and process until puréed and smooth. Add yogurt, lemon zest and juice, some salt and pepper to the processor and continue mixing until smooth and combined.
Chill dip and serve cold with veggies alongside for dipping.