Wash and peel the potatoes if desired. Cut each potato into 1/3–1/2-inch thick shoestring or standard fry cuts so they cook evenly. Place cut potatoes into a large bowl of cold water (about 4 cups) and soak for 30 minutes to remove surface starch.

Rinse and dry

After soaking, drain the potatoes and rinse under cold water until water runs clear. Spread the fries on clean kitchen towels or paper towels and dry thoroughly — moisture prevents proper crisping.

First fry (blanch)

Heat 1 cup vegetable oil in a deep heavy-bottomed pot or fryer to 325°F (approx. 160°C). If you don't have a thermometer, heat until a small piece of potato sizzles gently. Fry the potatoes in batches (do not overcrowd) for 3–4 minutes per batch until softened and pale (not browned). Remove with a slotted spoon and drain on a wire rack or paper towels. Let rest 10 minutes.

Second fry (crisp)

Increase oil temperature to 375–400°F (190–200°C). Fry the blanched fries again in batches for 2–3 minutes until golden brown and crisp. Remove and drain on a wire rack or paper towels. Immediately season with kosher salt (about 1 tablespoon divided among batches) and freshly ground black pepper to taste.

Garlic-Gilroy Topping

Make garlic butter

While the fries are resting after the first fry or while doing the second fry, melt the unsalted butter with the extra-virgin olive oil in a medium skillet over medium-low heat. Add the finely minced fresh garlic and the Gilroy roasted garlic purée (or additional roasted garlic). Cook gently, stirring frequently, for 45–60 seconds until fragrant. Do not brown the garlic — you want a soft aromatic garlic butter. Remove from heat.

Combine seasoning

Stir the chopped parsley, lemon zest, red pepper flakes, toasted sesame seeds (if using), and about 3/4 cup of the grated Parmesan into the garlic butter mixture. Taste and adjust seasoning, adding finishing salt if needed. The mixture should be saucy but not watery.

Toss fries with topping

Place the hot fries in a large mixing bowl or on a serving tray. Pour the garlic-parmesan butter evenly over the fries and toss gently but thoroughly to coat each fry. If using a tray, drizzle and then toss with tongs or two spatulas. The residual heat will meld flavors and slightly melt the Parmesan.

Finish and serve

Transfer fries to a serving platter. Sprinkle the remaining 1/4 cup grated Parmesan over the fries and garnish with a little extra chopped parsley and a pinch of red pepper flakes if desired. Serve immediately with lemon wedges on the side for optional brightening.