Preheat oven to 375F. Line baking sheet with parchment.
Bring large pot of salted water to boil. Add potatoes and reduce the heat. Simmer until tender, 6-10 minutes. Drain and cool. Slice thin and set aside.
In small saucepan, melt butter over medium low heat. Add garlic and saute until soft. Stir in flour and cook for 30 seconds. Whisk in cream and cook, stirring often until warm and thickened, about 6-8 minutes. Stir in gorgonzola and melt. Season with salt and pepper. Remove from heat.
Place flatbread on baking sheet and brush with olive oil. Spoon gorgonzola cream on crust and spread almost to edges.
Lay prosciutto on top. Next layer sliced potato, dust with parmesan.
Bake until toasted, 12-15 minutes. Sprinkle basil on top.