3 tablespoons butter, divided
6 large fresh sage leaves
1/3 cup walnut halves, coarsely chopped
1 medium yellow onion, diced
1/2 cup (2 ounces) diced pancetta or bacon
1 1/2 pounds Brussels sprouts, sliced thinly
1/4 cup water, chicken, turkey, or vegetable broth
2 teaspoons sherry or cider vinegar
Heat 2 tablespoons of the butter in a small (8-inch) skillet over medium heat. As soon as the foam subsides, add the sage leaves to the skillet and fry for about two minutes, turning once with a fork or tongs. Don’t let the leaves get brown — they are done when they stop sizzling and no more water is bubbling to the surface. Transfer the sage leaves to a paper towel-lined plate, sprinkle with a pinch of salt, and set aside. Do not wipe out the skillet.
Turn the heat down to medium-low, then add the chopped walnuts to the skillet. Cook the walnuts in the butter until they’re aromatic and a bit toasted, about 3 minutes. The butter will be well-browned. Turn off the heat and set the skillet aside.
In a large (12-inch) skillet or sauté pan, heat the remaining 1 tablespoon of butter over medium heat. Add the diced onion and pancetta. Sauté until the onions are soft and just beginning to brown, about 10 minutes. Add the Brussels sprouts, stirring to mix evenly with the onions and pancetta. Pour in the water or broth, cover the pan, and let cook for 10 minutes.
Remove the lid and turn the heat up to medium-high. Sauté until all of the liquid is evaporated and the hash is beginning to sizzle, about 5 minutes. Turn off the heat. Pour in the vinegar and stir everything one last time, using a spoon to nudge the browned bits from the bottom of the pan.
Transfer the hash to a serving bowl and top with the walnuts and sage, crumbling the sage leaves evenly over the top. Serve hot.