Sourdough Rye Sharp Cheddar Burger Buns

Steps

1. Starter, the day before: feed your sourdough starter in the morning and leave it at about 75°F (24°C); it should peak, doubled and bubbly, in 4 to 6 hours. Measure the sourdough starter for the dough at its peak.
2. Divide the cheddar before you begin: set aside about 130 g (roughly three quarters) for the dough and the remaining 50 g (one quarter) for the tops.
3. In a large bowl, whisk the water, honey and sourdough starter until the starter dissolves.
4. Add the rye flour, bread flour, salt and onion powder and mix with a sturdy spatula until no dry patches remain. This is about 74% hydration and 2% salt, counting what the starter contributes. Cover and rest 30 minutes.
5. Add the softened butter and squeeze it into the dough with wet hands until absorbed, then fold in the reserved dough portion of the cheddar until evenly spread. Rye dough is sticky and paste-like, so keep your hands wet rather than dusting the counter.
6. Bulk rise, covered, at about 75°F (24°C) for 3½ to 4 hours. In the first 2 hours, do 3 sets of stretch-and-folds 30 minutes apart with wet hands, then leave it alone. It is ready when it has grown by about half, looks puffy and shows bubbles on the surface.
7. Line a baking sheet with parchment. Turn the dough onto a lightly wet counter and divide it into 12 pieces of about 110 g. With damp hands, round each into a smooth ball, place on the sheet, and press each gently into a 3½-inch disk.
8. Cover the buns and cold-proof them in the fridge overnight, 10 to 14 hours.
9. In the morning, take the buns out and let them sit at about 75°F (24°C) for 60 to 90 minutes, until puffy and a poked dent springs back slowly. Meanwhile, preheat the oven to 400°F (200°C).
10. Brush the buns with the beaten egg, scatter on the remaining tops portion of the cheddar, then sprinkle with the sesame seeds.
11. Bake 20 to 24 minutes, until deep golden, the cheese is crisp at the edges, and the center of a bun reads 190°F (88°C).
12. Cool the buns completely on a rack, at least 1 hour so the rye crumb sets, before slicing in half for burgers.