Homemade hot dog buns, with grilled hot dogs

Whisk half a cup of milk, half a cup of water and 50 g of bread flour until the flour dissolves and the liquid is smooth.

Cook over medium-high heat, whisking constantly, until the flour releases its starches and pre-gelatinizes and the mixture goes from liquid to a thick, almost solid paste like smooth mashed potatoes.

Transfer to a bowl and cool to room temperature at a minimum, stirring occasionally; the long mix heats the dough by friction.

In the stand mixer bowl with the dough hook, combine 490 g of bread flour, 10 g of kosher salt, a tablespoon of granulated sugar and the instant yeast.

Add the cooled paste, a quarter cup of water, a tablespoon of vegetable oil and two cold eggs, and mix on the lowest speed.

After about five minutes the dough pulls away from the bowl and is tacky but not sticky.

Still on the lowest speed, add four tablespoons of cold unsalted butter. Stop every few minutes and scrape the hook and the bowl. Total mix time 15 to 20 minutes.

Test with a moderate windowpane: stretched gently it should give a thin film light passes through, and it will tear if stretched hard.

Let rise an hour until doubled, or cover and refrigerate overnight for better flavour and texture.

Pat the cold dough down to degas it. Portion into 12 pieces of about 80 g.

Pre-shape: flatten each piece, gather the irregular ends to the centre, set it seam side down and drag it in small circles under a cupped hand until taut.

Bench rest about 10 minutes, covered.

Shape: turn domed side down, smash to elongate, roll up into a log pressing as you go, seal the seam with your thumbs, then roll out seam down to an even five and a half inch log with no tapered ends - press at the centre, not the outsides.

Transfer to a half sheet tray in two rows of six, evenly spaced, and flatten each slightly so they do not dome.

Cover loosely and proof about an hour 15, until more than doubled and touching; a poke should spring back leaving a slight indentation.

Heat the oven to 400.

Beat the remaining egg and brush a thin coat over the buns for shine and browning, working gently so the air bubbles do not pop.

Bake on the centre rack at 400 for about 20 minutes; these were done at 15, golden brown.

Light a chimney of charcoal, about 20 to 25 minutes, and grill the frankfurters until the casing is crisp and marked.

Split the cooled buns by tearing them apart in the centre for the pull-apart effect.

Dress: sauerkraut tucked in first so the bun absorbs the juices, then raw red onion, then mustard.