Preheat your oven to 425°F (220°C). Wash and cut fresh potatoes into thin fries. Toss with olive oil, salt, and pepper, then spread in a single layer on a baking sheet. Bake for about 25 minutes, flipping halfway.

Meanwhile, fill a saucepan with water and bring it to a gentle simmer. Add a splash of vinegar. Crack the eggs into individual cups and gently slide them into the water. Poach for approximately 4-6 minutes.

In a heatproof bowl, whisk together egg yolks and lemon juice. Set the bowl over a saucepan of simmering water and gradually whisk in melted unsalted butter until the sauce thickens, about 5-7 minutes.

Once the fries are crispy, remove them from the oven. Layer them on a serving plate, top with poached eggs, and drizzle with hollandaise sauce.

Serve immediately, garnished with optional toppings like grated cheese or sautéed vegetables.