Melt 1/2 tablespoon butter in a large skillet over medium-high heat. Add the onion and sprinkle with the sugar, 1/2 teaspoon salt, and pepper to taste. Cook, stirring occasionally, until soft and golden, about 10 minutes. Add the beer and continue cooking, stirring occasionally, until the onions are tender and the liquid is slightly syrupy, about 8 more minutes. Remove from the heat and stir in the corned beef, Worcestershire sauce and mustard.
Divide half of the cheese between 2 bread slices; top with the corned beef mixture, and the remaining cheese and 2 bread slices.
Melt the remaining 1 tablespoon butter in a large skillet over medium heat. Add the sandwiches and cook, pressing occasionally with a spatula, until the bread is toasted and the cheese melts, about 4 minutes per side, adding more butter to the pan if needed.