Preheat oven to 450F.
In a mixing bowl, mix together flour, salt and baking powder. Add 1/4 cup olive oil to the flour mixture. Stir with a fork just until olive oil is incorporated into flour. Do not overmix. Add milk, parmesan cheese and chopped ham to flour mixture. Stir until ingredients are combined.
Turn dough onto a lightly floured board. With a floured rolling pin, roll out the dough to about 1/4 inch thick. Cut the biscuits with a round biscuit cutter. Place on an ungreased baking sheet. Bake until lightly browned -- 12 to 15 minutes.
Combine the remaining 6 tablespoons olive oil, parsley, basil and chives in a small bowl. Allow the biscuits to cool slightly after removing from the oven. Cut biscuits in half and drizzle the olive oil mixture on the inside of each biscuit. Stuff each biscuit with two ham slices. Serve while still slightly warm.