In your large mixing bowl, combine the warm water (make sure it's not too hot, or you'll kill the yeast!), sugar, and active dry yeast. Give it a gentle stir. Let it sit for 5-10 minutes until it looks foamy and bubbly on top. This tells you your yeast is alive and ready to work its magic!
To the activated yeast mixture, stir in the salt and olive oil. Add 2 cups of the all-purpose flour. Stir with a wooden spoon or dough whisk until just combined and you have a shaggy dough.
While the yeast activates or just before adding flour, finely shred your cabbage. If using onion, finely chop it. You can sauté the onion in a little oil for a few minutes until softened before adding, or add it raw – raw will give a slightly stronger flavor. Add the shredded cabbage (and sautéed or raw onion, if using) to the shaggy dough mixture.
Begin adding the remaining flour, ½ cup at a time, mixing after each addition, until the dough starts to pull away from the sides of the bowl. It will still be sticky at this point, but manageable. You might not need all 4 cups, or you might need a touch more – it depends on your flour, humidity, etc.
Turn the dough out onto a lightly floured surface. Knead the dough for 8-10 minutes. Start by folding the dough towards you, pressing down and away with the heels of your hands, rotating slightly, and repeating. This develops the gluten, which is crucial for the bread’s structure. The dough should become smooth, elastic, and less sticky, though it might still have a slight tackiness. You'll feel a real difference in its texture. If it’s too sticky, add just a tablespoon of flour at a time.
Lightly grease your large mixing bowl with a little olive oil. Place the kneaded dough in the bowl, turning it to coat all sides with oil. Cover the bowl tightly with plastic wrap or a damp kitchen towel. Place in a warm place to rise until doubled in size, about 1 to 1.5 hours. A slightly warm oven (turned off) or a sunny spot on the counter works well.
Once the dough has doubled, gently punch it down to release the air. Turn the dough out onto your lightly floured surface. You can gently shape it into a round or oval loaf for a freeform bake, or shape it into a log and place it seam-side down in a greased 9x5 inch loaf pan.
Cover the shaped loaf (either on the baking sheet or in the pan) loosely with plastic wrap or a light kitchen towel. Let it rise again in a warm spot for another 30-45 minutes, or until it looks noticeably puffy and has almost doubled in size. While it's rising, preheat your oven to 375°F (190°C). If baking on a sheet, you can line it with parchment paper.
Place the loaf in the preheated oven. Bake for 30-40 minutes for a loaf pan, or 35-45 minutes for a freeform loaf. The bread is done when it's golden brown on top and sounds hollow when tapped on the bottom. If the top is browning too quickly, you can loosely tent it with aluminum foil.
Carefully remove the bread from the oven. If using a loaf pan, turn it out onto a wire rack immediately. If freeform, transfer it to the rack. Let the bread cool completely before slicing. Slicing hot bread can make it gummy inside! I know it's hard to resist, but trust me on this!