Thyme Onion Cheddar Rye Sourdough Boule

Steps

1. Day 1, morning: feed your sourdough starter from your own supply as you usually do, with equal weights of its usual feed and water, and leave it at about 75°F (24°C) for 4 to 6 hours, until it has doubled, is domed and bubbly, and peaks.
2. While the starter rises, warm the olive oil in a skillet over medium-low heat, add the onion and cook, stirring often, for 15 to 20 minutes until soft and golden. Stir in the thyme for the last minute, then spread the onion mixture on a plate to cool completely.
3. When the starter peaks, stir the sourdough starter into the water in a large bowl until milky. Add the rye flour and bread flour and mix with a wet hand or stiff spatula until no dry patches remain; the dough will be sticky and paste-like. Cover and rest 30 minutes.
4. Sprinkle the salt over the dough and squeeze and fold it in with a wet hand until evenly mixed. This dough is about 80% hydration and 2% salt, counting the starter's share of water and grain.
5. Bulk rise, covered, at about 75°F (24°C) for about 4 hours. After the first 30 minutes, do a set of stretch-and-folds with wet hands, lifting each side of the dough and folding it over the middle.
6. At the second set of stretch-and-folds, 30 minutes later, scatter half of the cheddar and half of the cooled onion mixture over the dough and fold them in. At the third set, 30 minutes after that, add the remaining half of the cheddar and the remaining half of the onion mixture and fold them in. Leave the dough untouched for the rest of the bulk rise, until it has grown by about half, looks puffy and shows bubbles on the surface; rye dough rises less than wheat dough.
7. Turn the dough onto a lightly wet counter and, with wet hands, gently tuck the edges under to shape a round boule. Place it seam side down on a sheet of parchment set inside a bowl.
8. Proof covered at about 75°F (24°C) for 1 hour, then cover tightly and cold-proof in the fridge overnight, 10 to 14 hours.
9. Day 2: place a lidded Dutch oven in the oven and preheat to 475°F (245°C) for 45 minutes.
10. Lift the cold dough on its parchment, score a cross on top with a sharp blade, and lower it into the hot Dutch oven. Cover and bake 25 minutes.
11. Remove the lid, lower the oven to 425°F (220°C) and bake 25 to 30 minutes more, until the crust is a deep mahogany brown and the center reads 205°F (96°C) on a thermometer.
12. Cool the loaf on a rack for at least 3 hours before slicing so the rye crumb sets, then cut into 12 slices.