Preheat oven to 400°F. Line a baking sheet with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, mix flour, baking powder, and sugar until combined. Add butter and mix until the pieces of butter are the size of peas.
Put pineapple on a paper towel to soak up excess juice and chop ham into small pieces. Add these to the flour and butter mixture and turn on the mixer until they are just mixed in.
In a small bowl, whisk milk and egg together and add to the mixer. Mix until a sticky dough is formed.
Turn onto floured counter and form into a ball. Flatten out with your hands and using a pizza cutter cut into 12 pieces. Transfer to baking sheet and top with cheese and a sprinkle of basil.
Bake for 22 minutes or until bottoms are a nice golden brown.