Bring 4 qts. water and salt to a low simmer in a large pot. Add potatoes and simmer until cooked through, 20–25 minutes. Remove, and refrigerate them, uncovered, until cold.
Once potatoes are chilled, cut them crosswise into 1⁄4-inch slices. Place a skillet over medium heat, and when it’s hot, add 1⁄4 cup olive oil. Add the potato slices and cook until potatoes are crispy and “golden-brown delicious,” as chef says, about 4 minutes per side. Remove and set aside.
Lower the heat and add garlic to cook, about 4–5 minutes.
Place potatoes on a plate, and pour garlic and remaining olive oil over them. Top with queso fresco.