In a large skillet, heat the oil over medium-high heat. Add the cabbage and cook until wilted, 5 minutes; season with the caraway seeds (if using), salt and pepper. Add 1/4 cup chicken stock, lower the heat and keep simmering.
In a medium saucepan, melt the butter over medium heat until foaming. Add the onions and bay leaf; season with salt and pepper. Cook, stirring occasionally, until the onions are light golden and very soft, about 15 minutes. Stir in the relish, vinegar and brown sugar; discard the bay leaf.
Preheat the broiler. In a small skillet, heat the remaining 1/4 cup chicken stock over medium heat. Turn off the heat and add the corned beef to warm through.
Arrange the 4 bread slices on a foil-lined baking sheet. Using a slotted spoon, transfer the cabbage, corned beef and onion mixture to the bread. Top with the cheese; broil until melted (top with the remaining 4 bread slices, if using). Serve with the mustard and pickles.