Preheat oven to 400F. Line a baking sheet with parchment paper and set aside.
In a large bowl, mix together the dry ingredients: all-purpose flour, baking powder, baking soda and salt. Using a box grater, grate the butter into the flour mixture. Transfer the bowl to the freezer while you gather the wet ingredients, about 5-7 minutes.
Measure out the milk and add the egg; whisk until combined. In a small bowl, make the egg wash, whisking together the egg and milk.
Grab the bowl out of the freezer, and gently break up the butter and combine with the flour, using your hands, until it resembles small peas. Add in the gouda cheese and toss to combine thoroughly. Add the buttermilk mixture all at once to the flour mixture. Mix until barely combined; and lightly knead the dough until it forms into one solid mass.
Sprinkle your kitchen counter with flour and dump the dough onto it. Press the dough into a 3/4-inch thickness. Form it into a rectangle and cut biscuits. You should end up with about 6 biscuits. Transfer them to the baking sheet. Brush the tops with egg wash and sprinkle with black pepper. Bake until fluffy and lightly golden brown, about 12 to 14 minutes.
To assemble the biscuit sandwiches, slice the biscuit in half. Smear one side with a bit of mustard, top with a slice of ham, add some glaze and add the other half of the biscuit. Repeat until you’ve built all of the biscuit sandwiches.