Mix the water, yeast, and flour until no dry flour remains. Cover and rest for 30 minutes.
Add the salt and olive oil; fold until incorporated. Cover and rest for 30 minutes.
Fold the dough two to three more times at 30-minute intervals, until smooth and elastic.
Transfer to a lightly oiled airtight container and refrigerate 12 to 72 hours.
Line a loaf pan or small sheet pan with parchment. Transfer the dough, cover, and rest at room temperature for 30 minutes.
Heat the oven to 430°F/220°C.
Spread the sun-dried tomato mixture over the dough, scatter the cheddar and thyme, and gently dimple the surface. Finish with coarse salt.
Bake until deeply golden, 22 to 24 minutes. For a crisper base, remove from the pan and bake directly on parchment 3 to 4 minutes more. Cool slightly, then slice.