Heat the olive oil in a large pot or Dutch oven over medium-high heat. Open the can of corned beef and slice it into bite-sized chunks or thin strips, depending on your preference. Once the oil is hot, add the corned beef and cook for 5 minutes, stirring occasionally, to develop some light browning and enhance the flavor. This step builds a flavorful foundation before the broth and vegetables join in. After 5 minutes, transfer the corned beef to a clean bowl and set aside.
Pour the beef broth into the same pot and bring it to a simmer. While the broth heats, cut the cabbage head into 1-inch thick wedges—this size allows the cabbage to steam evenly while maintaining structure. Once the broth is simmering, add the cabbage wedges, stir gently, and cover the pot. Steam for 5 minutes until the cabbage begins to soften but still has slight texture. The broth will infuse the cabbage with savory flavor while keeping it from becoming mushy.
Carefully drain the excess liquid from the pot, leaving just a thin coating of broth to keep the dish moist. Return the cooked corned beef from Step 1 to the pot with the cabbage. Sprinkle in the onion powder, garlic powder, salt, black pepper, and paprika, stirring everything gently to distribute the seasonings evenly. I like to add freshly ground black pepper here rather than pre-ground—it makes a noticeable difference in the final flavor. Cook everything together for 3 to 5 minutes, allowing the flavors to meld and the corned beef to warm through completely.
While the pot meal finishes cooking, prepare the sandwich filling if you're making corned beef sandwiches. Dice the celery into fine 1/8-inch pieces for a delicate texture that spreads easily. In a small bowl, combine the mayonnaise, relish, celery, and Dijon mustard, mixing until well blended. This creamy spread adds richness and tang that pairs perfectly with the savory corned beef. Cover and set aside until ready to assemble sandwiches.
For the traditional skillet dinner, transfer the corned beef and cabbage mixture directly to serving plates and enjoy immediately. For sandwiches, spread the mayonnaise mixture from Step 4 onto your bread of choice, then top with the warm corned beef and cabbage mixture. I find that serving the corned beef warm while the spread is cool creates a nice textural contrast. Add any additional toppings you prefer and serve right away.