Cooking time includes rising time. I don't own a Kitchenaid type mixer so the instructions are for hand kneaded bread. I imagine a mixer would work just fine for mixing and kneading. This is a great way to use up leftover mashed potatoes.
- In a small bowl sprinkle the yeast over 1 cup warm water and let it proof for 5 minutes, or until it is foamy.
- In a large bowl combine well 4 cups of the flour with the mashed potatoes and the salt until the mixture resembles coarse meal, add the yeast mixture, and stir the dough until it is combined well.
- Turn the dough out onto a floured surface and knead it, incorporating as much of the remaining 1/2 cup flour as necessary to prevent it from sticking, for 8 to 10 minutes, or until it is smooth and elastic.
- Form the dough into a ball, put it in an oiled bowl, and turn it to coat it with the oil.
- Let the dough rise, covered with plastic wrap, in a warm place for 1 1/2 hours, or until it is double in bulk.
- While the dough is rising, in a small bowl stir together the garlic, the rosemary, and the oil and let the mixture stand, covered.
- Turn the dough out into a well-oiled 15 1/2- by 10 1/2-inch jelly-roll pan, press it evenly into the pan, and let it rise, covered loosely, in a warm place for 45 minutes or less, or until it is almost double in bulk.
- Using a mandoline or hand-held slicer cut the red potatoes into paper-thin slices, arrange the slices on the dough, overlapping them, and brush them with the oil mixture, discarding the garlic.
- Sprinkle the focaccia with salt and pepper to taste and bake it in the bottom third of a preheated 400°F oven for 40 to 50 minutes, or until it is golden.
- Let the focaccia cool in the pan on a rack and serve it warm or at room temperature.