Step 1 Warm the olive oil in a large skillet over medium heat and cook the carrots, celery and onion until soft, 8 to 10 minutes. Add the garlic and cook until fragrant, about 3 minutes.
Step 2 While the vegetables are cooking, scrub the pig ears clean and cut away any knobby bits of cartilage so they will lay flat.
Step 3Place the pig ears in a single layer on top of the vegetables (they may overlap). Season with salt and add the water and dry white wine. Bring to a simmer, reduce the heat to low, cover and cook until the ears are very tender, about 3 1/2 hours.
Step 4Carefully remove the ears from the broth, place them on a parchment paper-lined plate, cover tightly with plastic wrap and refrigerate until firm, at least 2 hours. Save the flavorful broth for cooking beans. Once braised pig ears have been chilled, they can be tightly wrapped in plastic and frozen until ready to use.