Peel potatoes leaving some peel on the end for easier handling. Grate peeled part of potato. Measure out 3 cups and sprinkle with salt. Leave shredded potato in a strainer for 30 minutes to allow liquid to drain. Before adding to bread mixture, squeeze out any extra moisture.
Cook other potatoes until fork tender. Mash well without adding any milk, butter or salt.
Slice top of heads of garlic to expose most of the cloves. Drizzle with olive oil then scrunch up into foil package. Bake at 350° for 30-40 minutes until cloves are very soft and golden. When cool enough to handle, squeeze cloves out of skin and measure out ¼ cup.
In a large bowl or stand mixer, add shredded potatoes, mashed potatoes, garlic, salt and pepper, flour, baking powder, milk, melted butter and rosemary.
Preheat oven to 350° and ensure rack is set in middle of oven.
Knead with a dough hook in stand mixer or on floured surface by hand until dough comes together, about 5 minutes. Add extra flour if necessary if dough is sticking to surface or stand mixer bowl.
Divide dough evenly into 4 parts. On a lightly floured surface, roll each part into a circle and slightly flatten to somewhere between a ball and a disk, about 6 inches in diameter.
Place shaped dough onto a buttered baking sheet or parchment covered sheet and brush generously with beaten egg. Using a sharp knife, cut a cross into the top of each disk and sprinkle with extra kosher or Maldon salt.
Bake for 40 minutes on the centre rack of the oven until cooked through and lightly browned. Cool on a rack before slicing.