Line a 9-by-13-inch metal baking pan with parchment. Start with the measured cooked potato, completely cooled and free of lumps. Whisk the mashed potato, whole milk, water, egg and 40 g honey in a large mixing bowl until evenly combined. Liquids should feel barely warm.

Add the bread flour, instant yeast and salt. Mix until no dry patches remain, scraping the bottom thoroughly. The dough will look rough and feel sticky; keep all the measured flour in the bowl rather than reserving any for shaping.

Knead with a dough hook on low speed for 4 minutes. Add 50 g softened butter gradually, then knead for 6–8 minutes, until elastic and mostly smooth. A stretched piece should form a thin, translucent patch before tearing. Scrape down as needed.

Cover the bowl and allow 90 minutes for the bulk rise in a comfortably warm spot. The dough should roughly double and look aerated. Begin checking earlier if your room is warm; visible expansion matters more than the clock.

Rest the dough for 10 minutes, covered, after gently pressing out large bubbles. Divide into 15 equal pieces, approximately 74 g each. On an unfloured surface, tuck each piece underneath and cup into a ball. Arrange seam-side down in 3 rows of 5.

Cover and allow 60 minutes for the final rise, until puffy and nearly touching. A gentle fingertip indentation should return slowly. During this rise, preheat the oven to 350°F with a rack in the center.

Bake for 25 minutes, until golden and a center roll registers 190°F internally. Loosely tent with foil if browning quickly. Melt the remaining 20 g butter and stir in the remaining 20 g honey.

Brush the hot rolls with the honey butter. Cool in the pan for 10 minutes, then lift onto a rack using the parchment and cool for another 10 minutes before pulling apart.