For the biscuits: Preheat the oven to 475 degrees F.
Sift together the flour and salt into a large bowl. Add the butter and shortening and cut together with a pastry cutter. Gently stir in the buttermilk using a fork. Knead the mixture a few times with your hands until the dough comes together.
Tip the dough onto a floured surface and roll out to about 1/2 inch thick. Using a 3-inch round cutter, cut out 12 biscuits and transfer to a baking sheet.
For the topping: Brush the biscuit tops with 2 tablespoons of the melted butter and bake until golden, 13 to 15 minutes. Allow the biscuits to cool slightly, 4 to 5 minutes.
Meanwhile, whisk together the honey, Dijon, parsley and remaining 8 tablespoons melted butter in a small saucepan over medium heat. Bring to a simmer and remove from the heat.
For the sandwiches: Preheat the broiler.
Split the biscuits in half and return to the baking sheet cut-side up. Brush the cut sides with the honey butter. Place 2 halved ham pieces on the bottom of each biscuit and top each with a slice of cheese. Broil until the cheese is melted, 1 to 2 minutes. Carefully remove from the oven and pour over the remaining honey butter. Place the tops on the biscuits and serve.