Remove any damaged outer leaves from the 1 head green cabbage. Cut the cabbage into quarters, remove the tough core and slice each quarter into thick wedges or roughly 1 1/2-inch pieces. Keep the pieces large because they will soften considerably while braising.
Heat the 2 tablespoons unsalted butter and 1 tablespoon extra virgin olive oil in a large Dutch oven or deep skillet over medium-high heat. Working in batches if necessary, add the cabbage and let it cook undisturbed for 3 to 4 minutes per side, until the edges are deeply golden. Transfer to a plate.
Reduce the heat to medium. Add the sliced 1 yellow onion and cook for 4 to 5 minutes, until softened. Add the minced 3 cloves fresh garlic, 1 teaspoon coarse kosher salt, 1/2 teaspoon ground black pepper and 1/2 teaspoon smoked paprika. Cook for 30 seconds.
Stir in the 1 cup low-sodium chicken broth or vegetable broth, 1 tablespoon Dijon mustard, 1 tablespoon apple cider vinegar, 1 tablespoon honey and 1 teaspoon Worcestershire sauce. Scrape the bottom of the pan to loosen any browned bits.
Return the cabbage to the pan. Spoon some of the liquid over the top, cover and reduce the heat to medium-low. Simmer for 18 to 25 minutes, depending on how tender you like your cabbage. The cabbage should be tender enough to cut easily with a fork but not so soft that it loses all of its structure.
Remove the lid and simmer for another 3 to 5 minutes, until the braising liquid reduces slightly and coats the cabbage. Taste and adjust the salt, pepper or vinegar as needed.
Seasoned Breadcrumbs:
While the cabbage braises, melt the 2 tablespoons unsalted butter with the 1 tablespoon extra virgin olive oil in a skillet over medium heat. Add the grated 1 clove fresh garlic and cook for about 20 seconds.
Stir in the 1 cup plain panko breadcrumbs, 1/2 teaspoon smoked paprika, 1/4 teaspoon onion powder and 1/4 teaspoon coarse kosher salt. Cook, stirring frequently, for 3 to 5 minutes, until the breadcrumbs are golden and crisp.
Remove the breadcrumbs from the heat, cooling for about 5 minutes.
When slightly cooled, stir in the freshly grated 2 tablespoons Parmesan cheese and 1 teaspoon lemon zest.
Serve:
Transfer the braised cabbage to a serving platter, spoon some of the reduced braising liquid over the top and generously scatter with the crispy seasoned breadcrumbs and chopped 1 tablespoon flat parsley.
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Notes
Storage: Refrigerate leftovers promptly in shallow, airtight containers and use within 3–4 days. Keep any unused breadcrumb topping separate and refrigerated. Refrigerate within 2 hours of cooking, or within 1 hour when temperatures are above 90°F.Reheating: Warm the cabbage in a covered skillet with a splash of broth until it reaches 165°F throughout. Gently re-crisp refrigerated breadcrumbs in a separate skillet and add them after reheating.Freezing: You can freeze the cabbage without the topping, but expect a softer texture after thawing. Thaw in the refrigerator, reheat thoroughly and make fresh breadcrumbs for serving.