Place potato in a saucepan, and cover with water. Bring to a boil. Reduce heat, and simmer 15 minutes or until tender. Drain in a colander over a bowl, reserving 1 1/4 cups cooking liquid. Cool liquid to 110°. Mash the potato with a potato masher to measure 2 cups; set aside.
Combine warm cooking liquid and yeast in a large bowl, and let stand 5 minutes. Stir in the mashed potato. Lightly spoon flour into dry measuring cups; level with a knife. Gradually stir in 5 cups flour, salt, and pepper to form a stiff dough.
Turn dough out onto a lightly floured surface. Knead until smooth and elastic (about 10 minutes); add enough of remaining flour, 1 tablespoon at a time, to prevent dough from sticking to hands. Gently knead in cheddar and Asiago.
Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 30 minutes or until doubled in size. (Gently press two fingers into dough. If indentation remains, the dough has risen enough.) Punch dough down; cover and let rest 5 minutes. Divide dough in half. Working with one portion at a time (cover the remaining dough to prevent drying), roll each portion into an 11 x 7-inch rectangle on a floured surface. Roll up each rectangle tightly, starting with a long edge, pressing firmly to eliminate air pockets, and pinch seam and ends to seal. Place dough rolls, seam sides down, in 2 (8 x 4-inch) loaf pans coated with cooking spray. Cover and let rise 45 minutes or until doubled in size.
Preheat oven to 375°.
Uncover dough; bake at 375° for 1 hour or until loaves are browned on bottom and sound hollow when tapped. Remove from pans; cool on a wire rack.