Preheat the oven to 500 degrees F. Place a heavy large baking sheet in the oven until it is hot. Using a sharp chef knife, trim the potatoes to form rectangles. If desired, save any trimmings for another dish, such as for mashed potatoes. Cut the potatoes into fries that are 3/4-inch thick and 3 to 4 inches in length. Place the potatoes in lemon water until cooking to prevent them from browning.
Drain the water from the potatoes and place the potatoes on a large baking sheet lined with paper towels. Using paper towels, pat the potatoes until they are dry.
Toss the cut potatoes, thyme, rosemary, garlic, and smoked paprika with 2 tablespoons of the olive oil in a large bowl to coat the potatoes. Season with salt and pepper. Line the preheated baking sheet with a silicone baking mat. Arrange the potatoes in a single layer on the mat.
Roast the potatoes for 8 minutes. Remove the fries from the oven and turn them over as needed so that they brown evenly. Drizzle with the remaining 1 tablespoon of olive oil and return the fries to the oven and continue roasting until golden brown and tender, about 8 minutes.
Meanwhile, finely chop the garlic clove in a food processor. Add the yolks, red wine vinegar, and Dijon mustard and blend until smooth and fluffy, about 1 minute.
With the machine running, slowly add the oil in a thin steady stream until the aïoli is thick and creamy. If the mixture is too thick, add a little water to thin it to the desired consistency.
Stir in the parsley. Season the aïoli to taste with salt and pepper.
Remove the fries from the oven and lay the fries on another baking sheet lined with paper towels to absorb any excess oil; discard the thyme stems, rosemary, and garlic.