In a bowl, mix together boiled potatoes, ham, 1 piece egg, and 1/4 breadcrumbs and salt
In a pan, simmer 1/2 of beer and grated cheese. Stir until melted and add to the potato mix. Then form into 1 inch balls. Dredge balls in beaten egg then in remaining breadcrumbs. Store in the chiller or freezer for 15 minutes.
Heat hot oil in a saucepan then fry croquettes until golden brown, about 3 minutes each.
Make sauce by simmering remaining beer until reduced by half. Add BBQ sauce and simmer for 1 more minute.