• Adjust the oven rack to the middle of the oven.
• Place the bread on a sheet pan. Brush the melted butter onto the slices of bread. Place into the oven and toast at 350 degrees for 4-6 minutes. Remove from the oven.
• In a saucepan melt the 2 tablespoons of butter. Whisk in the flour and let cook for 2 minutes. Add the dry mustard and salt. Whisk to combine.
• Add the stout and Worcestershire to the mixture and continue to whisk until combined. Add the cheese and let melt, stirring occasionally about 2-3 minutes.
• Remove from the heat and while whisking constantly, add the egg yolks one at a time. Continue to whisk until all ingredients are incorporated. Spread the sauce onto the toasted bread. Place back into the oven and broil for 1-2 minutes, or until bubbly and browned.
• Remove the Welsh Rarebit from the oven. Slice the bread in half, horizontally. Place one patty on top of the broiled cheese mixture (if adding additional toppings, like caramelized onions, place on top of the cheese mixture first). Add additional cheese sauce to the burger (if desired) and then top with the remaining half of the welsh rarebit. Broil for 1 minute to serve with a crispy top, or skip this step. Serve warm and immediately.

for the burger patty

• Heat a cast iron griddle on the cooktop or grill. The temperature should be medium-high on the cooktop and 350-450°F for the grill.
• In a large bowl, gingerly yet thoroughly, combine the ground beef, salt and pepper. Form into 2 1/2-inch round balls and place on a parchment-lined rimmed baking sheet.
• Place 2 tablespoons of butter onto the griddle. Once the butter is melted, add the meat balls to the griddle. With a canola oiled spatula (or a hamburger press) lightly smash the patty to desired thickness. Cook for 2 minutes and flip. Cook the remaining side for an additional 1 to 2 minutes to achieve desired doneness.
• Remove the patties from the grill and continue this process until all meat balls have been cooked.