Combine yeast, sugar, and water in a bowl. Leave to bloom for 10 minutes.
Combine the gluten-free flour, xanthan gum, and salt in a bowl.
Add the olive oil and active yeast mixture into the dry ingredients.
Knead the dough on a lightly floured surface.
Set the dough to rise in a lightly oiled bowl. Leave for an hour.
Transfer the dough onto a floured surface and flatten to approximately 1mm thickness with a rolling pin.
Cut the dough into 4"x6" rectangular pieces.
Put the cheese and ham on top of one rectangular piece of dough.
Cover with another cut and press on the sides to seal.
Repeat for remaining dough.
Bake calzones for 15-20 minutes at 425F.