For the beer cheese: In a saucepan, add the cheese, beer, oil, Dijon, Worcestershire and cayenne and heat over medium heat until melted and smooth. Bring to room temperature before serving. Use immediately or refrigerate up to 3 days.
For the biscuits: Preheat the oven to 425 degrees F. Line a rimmed baking sheet with parchment paper.
Put the flour, baking powder and salt in a food processor. Pulse until combined. Add the cold cubed butter and pulse until the butter is cut into pea-sized bites. Add the buttermilk and pulse until the dough just begins to come together, then turn out onto a floured board. Knead the dough a few times with your hands to bring together, then roll out into a 1-inch-thick disk. Punch out with a 1-inch biscuit cutter and arrange 1 inch apart on the prepared baking sheet. Brush with melted butter. Bake until golden brown on the underside and light golden on top, 16 to 18 minutes. Transfer the biscuits to a rack to cool at least 10 minutes.
For the sandwiches: Carefully split each biscuit through the middle. Fold a piece of ham on the bottom and dollop beer cheese on top. Sprinkle with scallions and sandwich with the top of the biscuit.