Heat the oven to 425°F (220°C) and line a large baking sheet with parchment.
Cut the carrots into sticks about 3 inches long and 1/2 inch thick, so they cook evenly.
Toss the sticks with olive oil, cumin, paprika and salt, and spread in a single layer with space between them.
Roast for 22–25 minutes, turning once halfway, until tender and browned at the edges.
Meanwhile, stir the yogurt, tahini, lemon juice, garlic and a pinch of salt together, adding a spoonful of water if it is too thick.
Sprinkle the carrots with herbs and serve warm with the dip.