In a pot over medium-high heat add the beer, vinegar, sugar, salt and peppercorns. Bring to a simmer, stirring just until the sugar and salt dissolve, remove from heat.
Add the peppers to an airtight container, add a few sprigs of dill.
Add the onions to a separate container, add a few sprigs of dill.
Pour the cooled brine over the onions and the peppers, making sure all vegetables are submerged.
Chill for at least 24 hours prior to using.
Preheat the oven to 350°F.
Add the bottom portion of the buns into a baking dish. Spread with mustard.
Top in an even layer with ham, pulled pork, peppers, onions, then cheese.
Place the top on the buns, brush with melted butter.
Place another baking dish on top of the buns, press down firmly. Keeping the second pan on top of the buns, place the entire thing in the oven.
Bake until the cheese has melted, about 12-15 minutes.