Instructions

For the Buns:

1. Place potatoes in medium saucepan and add water just to cover. Bring to boil over high heat; reduce heat to medium-low and simmer until potatoes are cooked through, 8 to 10 minutes. You'll know they're done when a sharp knife goes through the potatoes without any resistance.
2. Transfer 5 tablespoons of the potato cooking water to a small bowl to cool. Drain the potatoes, reserving aside a few more tablespoons of the water in another small bowl; you might need them later.
3. Return potatoes to the saucepan and place over low heat. Cook, stirring occasionally, until any surface moisture has evaporated and the potatoes look dry, about 1 minute.
4. Remove from heat. Process potatoes through ricer or food mill or mash well with potato masher. Measure 1 very firmly packed cup (8oz) of potatoes and transfer to a medium bowl. Stir in butter until melted. Reserve any remaining potatoes for another use.
5. In the bowl of a standing mixer (or a large bowl if kneading by hand) whisk together the flour, sugar, yeast and salt.
6. Add warm potato mixture to flour mixture and work it in with hands until well combined (some large lumps are OK)
7. Add the egg and the reserved 5 tablespoons of potato water; mix with dough hook (or wooden spoon) on low speed until dough is soft and slightly sticky, 8 to 10 minutes. The dough will start out looking very dry and tough and having a hard time getting kneaded, but it will soften and get stickier as the mixing progresses. When finished kneading, the dough should stick to the bottom of the mixing bowl but clears out the sides and feel tacky. If the dough feels dry and not tacky to the touch, add a little bit of the extra potato water to soften it up.
8. Shape the dough into a ball and place in a lightly oiled container, flipping and turning once to get it well oiled. Cover tightly with plastic wrap and allow to rise in a *warm place until almost doubled in size, 30 to 40 minutes.
9. Meanwhile cut and cook burgers, as directed below.
10. Turn out the dough onto work surface, dusting with flour ONLY if dough is too sticky to handle comfortably. Pat gently into an 8inch square of even thickness. Using bench knife or chef's knife, cut the dough into 9 equal piece (3 rows by 3 rows). Separate pieces and cover loosely with plastic. Working with one piece at a time, while the rest is covered, cut each piece into 3 pieces, ending up with 27 (1oz) pieces. Return all pieces under the plastic to prevent dough from drying out.
11. Working with one piece of dough at a time and keeping remaining pieces covered, form dough pieces into smooth, taut rounds. (To round, set piece of dough on unfloured work surface. Loosely cup hand around and, without applying pressure to dough, move hand in small circular motions. Lightly dust fingers with flour if dough sticks to hands).
12. Cover rounds with plastic and allow to rest for 15 minutes.
13. Line 17X13inch baking sheet with parchment paper. On a lightly floured surface, firmly pat down each dough round into a flat disk. Place a slice of pickle in the center, followed by a cooled mini burger, then top it with the quartered slice of cheese.
14. Gather up the dough on top of the filling, pressing the dough over itself to seal. Turn upside down then place on the prepared baking sheet, seem-side down. Repeat with the rest of the dough.
15. Cover loosely with plastic and let rise at room temperature until almost doubled in size and the buns' sides touch one another, 30 to 40 minutes. While the rolls rise, adjust oven rack to middle position and heat oven to 425F/220C.
16. Brush rolls gently with heavy cream and sprinkle with sesame seeds if using.
17. Bake rolls until deep golden brown, 10 to 13 minutes, rotating baking sheet halfway through to ensure even brownness. The tops will feel hard at first, then will soften up after a few minutes.
18. Transfer baking sheet to wire rack and let cook for 5 minutes. Then transfer rolls from baking sheet to wire rack to avoid soggy bottoms.
19. Serve warm with your favorite burger condiments.

Preparing the burgers:

1. Using a small round biscuit or cookie cutter (1 3/4inch or 4 1/2cm in diameter), cut 4 rounds in each burger patty. Gently gather up the remaining scraps of meat into a large patty, and cut more rounds from it. You should end up with 27 mini burger patties (I was able to get my 27 rounds from 5 1/2 burgers, but amounts will vary according to the size of the patty)
2. Cook the mini burgers on a nonstick skillet to the doneness of your liking. They will NOT continue cooking in the oven. Let cool before stuffing in the buns.