1 egg yolk, blended with 2 Tbsp water (for glaze, optional)
Add yeast to warm water and let stand 10 minutes. In a large measuring cup or in a medium-sized saucepan, heat milk and butter to 135°F.,(1 1/2 minutes in a microwave and 4 minutes in a saucepan on medium heat). Pour this liquid into a blender and add mashed potatoes, potato water, sugar, and salt. Blend for 30 seconds.
Pour into a large mixing bowl and add Best for Bread flour and mix well (you may use a mixer). Now add the egg and proofed yeast and blend by hand. Add all purpose flour to make a soft dough. On a lightly floured surface, knead until smooth and satiny, 10 minutes by hand, or 4 minutes in an electric mixer or food processor fitted with dough hook. Put dough in greased bowl, turning to coat thoroughly. Cover with damp towel and allow to rise in a warm, draft-free place until doubled, approximately 1 hour.
Knead down. Turn dough onto a floured surface. Divide into 6 equal portions and let rest for 10 minutes. Grease two, 9 x 5 x 3 inch loaf pans.
Roll each portion into a long rectangle, 16 x 4 inches, and sprinkle with 1/3 cup shredded cheese. Roll up rectangle to form a rope. Roll out the remaining portions and repeat. Take 3 ropes and braid together, being careful not to stretch dough. Place in a prepared loaf pan. Cover with a damp towel and allow to rise in a warm, draft-free place until doubled about 1 hour. Brush with egg yolk and water mixture and sprinkle with poppy seeds, if desired.
Preheat oven to 375°F. bake for 30 minutes, or until top is golden brown. Remove from pans and cool on racks.