DAY 1 (afternoon):

• Feed your sourdough starter in the afternoon, 4 to 6 hours before you plan to mix, so it's active, bubbly and roughly doubled.
• If your pumpkin puree looks watery, blot it with kitchen paper first. Canned brands vary a lot in moisture, and a wet puree will throw the dough off.

Mix The Dough:

• In the bowl of a stand mixer, combine the flour, brown sugar and salt. Add the starter, pumpkin puree, oil and 90g of the water. Mix on low speed for 5-7 minutes until it comes together.
• This will feel like a much stiffer dough than most sourdough recipes, and that's correct. Bagels are a low-hydration dough by design, it's what gives you the dense, chewy crumb rather than an open, holey one. It should be firm and only just tacky, not sticky. Add the reserved splash of water only if it genuinely won't come together.
• Knead on medium speed for 8-10 minutes until smooth and dense. It won't stretch as dramatically as a windowpane test on a wetter dough, but a small piece should stretch thin enough to see light through before tearing.

Bulk Fermentation:

• Put the dough in a lightly oiled bowl, cover it and leave it at room temperature for 8-10 hours, or until it has increased by about 60-70%. Mark the starting level with a rubber band or a piece of tape on the bowl so you can see the rise. It's a stiff dough and it takes a while, so don't expect it to look billowy. Don't put the dough in the fridge. The chill comes after shaping.

DAY 2:

Shaping:

• Divide the dough into 6 x 137 g or 8 x 103g pieces. Shape each into a smooth, tight ball, then push a floured finger or thumb through the centre and gently stretch the hole to about 5 cm across. It will shrink back as the dough proofs and boils, so go a bit bigger than you think you need.
• Or use the rope method, if you prefer it: roll each portion into a 20 cm rope, wrap it around your hand with the ends overlapping by a few centimetres, then roll the seam against the counter to seal it closed.

Second Rise:

• Place the shaped bagels on a parchment-lined, lightly oiled tray. TIP: place each bagel on a separate square of parchment paper, so you can pick each one up individually later.
• Cover loosely and leave them at room temperature, 22-23°C (72-73°F), for 1½ to 2½ hours. They're ready when they look puffy and feel soft, and a floured finger pressed into one leaves a dent that fills back in slowly. They won't double. Start checking at 1½ hours, then every 15 minutes.

Chill:

• Cover the tray (a large reusable bag or lightly oiled cling film works) and put it in the fridge, at about 4°C (39°F), for 1-2 hours. This firms the bagels up so they hold their shape in the water and lift out of it cleanly.

Prepare Toppings:

• Mix the sugar and spices in a small bowl for the sweet topping. Mix the pumpkin seeds, rosemary and sea salt for the savoury topping.

Boiling:

• Preheat the oven 220°C (425°F). Line one or two baking trays with parchment.
• Bring the 2 litres of water to a rolling boil in a wide pot. Stir in the bicarbonate of soda and the brown sugar or malt syrup, it will fizz up, that's normal.
• Working in batches of 2-3 so you don't crowd the pot, boil the bagels for 30 seconds per side (up to 45 seconds a side if you want an even chewier crust). Lift out with a slotted spoon, let the excess water drain off, then place back on the lined tray.

Topping:

• Top the bagels while they're still tacky from boiling, this is what makes the topping stick without needing an extra egg wash step on the sweet ones.
• Sweet: brush the warm maple syrup over 3 bagels, then sprinkle the sugar mixture on generously and pat it in.
• Savoury: brush 3 bagels with the beaten egg, then scatter over the pepitas, rosemary and flaky salt, pressing gently so they hold on.

Baking:

• Bake for 15-16 minutes if you have 8 smaller ones, or 18-21 minutes if you have 6 larger ones, until deeply golden and the base sounds hollow when tapped. The sweet ones tend to colour a touch faster because of the sugar, so check them from the 15-minute mark and tent loosely with foil if they're getting ahead.
• Cool on a wire rack for at least 15 minutes before slicing, cut into them too soon and you'll get a gummy crumb instead of a chewy one.