Store-bought egg bagels usually contain yellow food coloring, so don't be discouraged by this paler homemade version. The flavor is superior to anything at the market.

1. Peel and quarter potato, place in a small saucepan, cover with cold water, and bring to a boil. Cook until tender, drain, and reserve liquid. Mash with a fork and set aside. In a large bowl, combine 1 cup potato water, sugar, and yeast. Stir to dissolve and let stand until foamy, about 10 minutes.

2. Add mashed potato, 4 eggs, oil, ½ teaspoon salt, and enough bread flour to create a firm dough. Add flour only to reduce stickiness. Turn out onto a floured surface and knead 8–10 minutes.

3. Return to bowl, dust the top with flour, and cover with plastic wrap. Rise at room temperature until doubled in volume, about 1 hour.

4. Spray a baking sheet with pan spray and sprinkle with cornmeal. Turn risen dough onto a floured surface. Shape into a rope, about 3″ thick. Slice into 2″ pieces, then roll each into a tight ball. Leave balls on the floured surface, dust with flour, cover loosely with plastic wrap, and proof for 10 minutes.

5. Preheat oven to 425°F. Combine milk and 1 quart water in a large, deep skillet. Bring to a boil, then reduce to a simmer. Working with one roll at a time, poke your finger down through its center, and on a well-floured surface, begin spinning the roll to open up a large center hole. Make the hole large, as it will close in during baking.

6. Drop each bagel into liquid, and poach 30 seconds on each side. Remove, tap off excess liquid, then place on baking sheet, seam-side down. Mix remaining egg with a pinch of salt and brush lightly onto bagels. Place a pan of water on the oven floor, and bake until brown, 20–25 minutes. Cool completely on a rack.