Put the potatoes and garlic cloves in a saucepan and cover with cold water. Salt the water and bring to a boil; cook until the potatoes are beginning to fall apart when pierced with a fork, about 10 minutes. Drain the potatoes and put them back into the hot pan. Shake the pan and let the potatoes cool to room temperature; transfer them to a mixing bowl.
Add the mustard to the potatoes, and mash with a spoon or potato masher until smooth. In a small bowl, mix the flour, parmesan, ginger, and a healthy pinch of salt and pepper together and sprinkle it over the potatoes. Mix the potatoes very well; taste and add more salt and pepper if necessary.