Rinse the cubed potatoes in cold water. This was something I've not done before. I know it rinses off some of the starch and maybe that had something to do with the fantastic texture these had!
Heat the butter and oil over medium heat in a skillet until hot, then add the potatoes and stir. Cover and cook the potatoes until browned all over, stirring now and then. He said 10 minutes but mine took more like 20 (and I think my cubes were smaller than 1 inch too!)
Once the potatoes are nicely browned, add the peeled garlic cloves and cook another 10 minutes, covered, stirring now and then.