Dry the duck skin. Then add them skin side town to a cast-iron, enameled cast-iron pan, dutch oven (you do not need a lid), or heavy bottomed stainless steel pan over medium heat. You do not need oil because the fat from the legs will become the oil for this dish. Season with salt and pepper. Cook until browned.
In the meantime, prepare your vegetables. Cut the fingerling potatoes in half, dice the onion, slice the ginger, and chop the garlic.
When the legs are browned, flip them and cook for 2-3 minutes. Then, transfer them to a plate.
Preheat the oven to 400F.
Without cleaning the pot/pan, turn the heat up to medium-high. Add all the vegetables to the pan, season with salt and pepper, and cook until they start to brown, 10-15 minutes.
Add the duck legs back into the pan, skin side up. Add enough sake to go at least half way up the duck legs. DO NOT COVER THE DUCK LEGS WITH THE SAKE. You want to make sure that skin stays crispy.
Transfer the whole pan to the oven. Cook for 40 minutes, then lower the heat to 350F and cook for an additional 30 minutes. The skin should stay crispy (don't cover the pan!) and the legs should be tender.
Notes
You do not need a lid for the pan/pot you choose. If you cover the duck while it is cooking, the skin will no longer be crispy.You do not need any additional oil in this recipe because the duck legs have fat that you render out while browning them. Then, you cook the vegetables in the rendered duck fat.Cooking method adopted from Mark Bittman's Crisp-Braised Duck Legs.