Position the racks in the upper and lower thirds of the oven and preheat oven to 425 degrees. Line two rimmed baking sheets with parchment paper.
Using a sharp chef’s knife, cut the top and bottom off the sweet potatoes and stand them on one of the flat sides. Cut each into thin planks, ¼-inch thick, and then into matchsticks. Add the potatoes to a large mixing bowl and toss with the olive oil. Sprinkle with the starch, salt, and paprika, and toss until well coated.
Divide the fries among the prepared baking sheets and arrange in an even layer, making sure there’s space between each fry. Bake for 20 minutes, swapping the baking sheets from top to bottom halfway through, until nicely browned (but not blackened at the tips). Remove from the oven and toss the potatoes to redistribute. Return to the oven for about 5 minutes until crispy. Allow to cool for a few minutes on the pan before transferring to a serving platter or parchment paper cone.
While the fries are baking, make the aioli. In a small mixing bowl or bowl of a food processor, whisk or pulse the egg yolks, mustard, lime juice, sriracha, and garlic until smooth. Working slowly, add 1 teaspoon of the olive oil and whisk or pulse until incorporated. Repeat with 2 additional teaspoons. Once the oil is emulsifying easily, slowly drizzle in the remaining olive oil, follwed by the coconut oil, whisking or ulsing throughout until thick. Season with the salt.
Serve the hot fries alongside the coconut oil-sriracha aioli for dipping.