Instructions

Place potato in medium saucepan and cover with 1 inch cold water. Bring to boil over high heat, then reduce heat to maintain simmer and cook until potato is just tender (paring knife slipped in and out of potato should meet little resistance), 8 to 10 minutes.
Transfer ¾ cup (6 ounces; 171 grams) potato cooking water to liquid measuring cup and let cool completely; drain potato. Return potato to saucepan and place over low heat. Cook, shaking saucepan occasionally, until any surface moisture has evaporated, about 30 seconds. Off heat, process potato through ricer or food mill or mash well with potato masher. Measure 1 cup (8 ounces; 227 grams) very firmly packed potato and transfer to bowl (discard remaining mashed potato or save for another use). Stir in butter until melted and let mixture cool completely before using.
Whisk flour, yeast, and salt together in bowl of stand mixer. Add mashed potato mixture to flour mixture and mix with your hands until combined (some large lumps are OK). Using dough hook on low speed, slowly add potato cooking water and mix until cohesive dough starts to form and no dry flour remains, about 2 minutes, scraping down bowl as needed. Increase speed to medium-low and knead until dough is smooth and elastic and clears sides of bowl, about 8 minutes. Reduce speed to low; add dill; and mix until incorporated, about 1 minute.
Transfer dough to lightly floured counter and knead by hand to form smooth, round ball, about 30 seconds. Place dough seam side down in lightly greased large bowl or container; cover tightly with plastic wrap; and let rise until doubled in size, 1 to 1½ hours.
Grease 8½ by 4½-inch loaf pan. Press down on dough to deflate. Turn out dough onto lightly floured counter (side of dough that was against bowl should now be facing up). Press and stretch dough into 8 by 6-inch rectangle, with long side parallel to counter edge. Roll dough away from you into firm cylinder, keeping roll taut by tucking it under itself as you go. Pinch seam closed and place loaf seam side down in prepared pan, pressing dough gently into corners. Cover loosely with greased plastic and let rise until loaf reaches ½ inch above lip of pan and dough springs back minimally when poked gently with your knuckle, 20 to 30 minutes.
Adjust oven rack to lower-middle position and heat oven to 350 degrees. Using sharp paring knife or single-edge razor blade, make one ½-inch-deep slash with swift, fluid motion lengthwise along top of loaf, starting and stopping about ½ inch from ends. Gently brush loaf with egg wash and bake until loaf is golden brown and registers 205 to 210 degrees, 45 to 50 minutes, rotating pan halfway through baking. Let loaf cool in pan on wire rack for 15 minutes. Remove loaf from pan and let cool completely on wire rack, about 3 hours, before serving.