Cut the carrots into quarters lengthwise, then thirds crosswise. Place on a parchment paper-lined baking sheet in a single layer and drizzle with the olive oil and sprinkle with 1/4 teaspoon salt. Roast until they just start to brown, 15 to 20 minutes. Remove the carrots from the oven.
While the carrots roast, prepare the dip: Whisk together the tahini, nut butter, lemon juice, paprika, garlic powder, cayenne pepper, 1/4 teaspoon salt and 1/3 cup water in a small bowl until smooth. Alternatively, blend them in a blender until smooth. Scrape into a serving bowl and sprinkle with sesame seeds.
Serve the carrot fries immediately with the dip. The dip can be refrigerated in an airtight container for up to 3 days.