Peel and slice potatoes ⅛-inch thick using a sharp knife or mandoline. Add to a large saucepan and cover with 1 inch of salted water. Bring to a low boil over medium-high heat and simmer for 5 minutes. Remove potatoes with a slotted spoon and set aside to cool for at least 10 minutes.
Meanwhile, trim and discard dark green ends off leeks and halve lengthwise, leaving root ends intact. Clean in cold water, checking for grit between layers. Once clean, slice into ¼-inch half-moons.
Warm a large skillet or sauté pan over medium-low heat. Add bacon fat and heat until rendered. Add leeks and season with salt and pepper, stirring to coat. Increase heat to medium and cook until leeks are slightly wilted and translucent, 5 to 6 minutes. Increase heat to medium-high and evenly spread leeks across the pan, pressing into the surface and up the sides to create a thin layer. Sear for another 5 to 6 minutes, or until edges begin to turn golden brown, stirring occasionally to prevent burning. Reduce heat to medium-low. Add cream, bay leaf, and another pinch of salt and black pepper. Stir, scraping up crispy bits stuck to the pan. Bring to just below a simmer, about 5 minutes, then cover and set aside.
Heat oven to 350°F.
Smash the garlic clove and rub over the interior of an 8 x 8-inch baking dish. Lightly grease the dish with butter. Using half the potatoes, fan out and layer slices on the bottom of the dish. Pour in half of the leek mixture, two-thirds of the cheese, and half of the chives. Repeat with remaining potatoes, leek mixture, and cheese for additional layers.
Combine breadcrumbs and olive oil in a small bowl and season with salt and pepper. Sprinkle over gratin.
Cover and bake for 30 minutes. Remove cover and continue baking for another 30 minutes, or until the potatoes are tender and the top is golden brown and bubbling. Cool for 10 minutes and dress with remaining chives.