Score the skin of the duck breasts in a crosshatch pattern using a sharp knife, being careful not to cut into the meat. Season both sides generously with salt and pepper.

Place the duck breasts skin-side down in a cold cast-iron skillet. Turn the heat to medium-low to slowly render the fat. Cook for 10-15 minutes until the skin is thin, golden, and crispy.

While the duck renders, soak the potato batons in cold water to remove excess starch, then pat them completely dry with paper towels.

Carefully pour the rendered duck fat from the skillet into a separate deep pot or frying pan. Add the vegetable oil to the duck fat and heat to 350°F (175°C).

Return the skillet with the duck to the stove over medium-high heat. Flip the breasts and cook the meat side for 3-5 minutes (for medium-rare). Remove from heat and let rest.

Fry the potatoes in the hot fat mixture in batches for 5-7 minutes until golden brown and crispy. Remove with a slotted spoon and drain on a wire rack.

Toss the hot fries immediately with extra sea salt, fresh thyme, and the smashed garlic. Slice the duck breast and serve alongside the fries.