Mix yeast, water, sugar, and ½ cup of flour together in a mixing bowl. Cover and let sit for 30 minutes or up to 2 hours until the surface resembles a sponge. 

Mix in remaining flour, salt, olive oil and cold water. Knead for five minutes with the dough hook attachment, or by hand, until a smooth but slightly sticky ball of dough is formed. If it seems too wet, knead a bit more flour into it.

Oil a large bowl and put the ball of dough into the bowl, then flip the dough over so the oiled side is up. Cover the bowl with plastic wrap or a kitchen towel and let sit in a warm place until doubled in size, 1 ½ to 2 hours.

After the dough has risen, you can punch it down and refrigerate it for a few hours, or overnight. Let it come to room temperature before continuing.

In a large sauté pan, lightly coated with oil, caramelize onions, with thyme sprigs, over medium-high heat until very soft, gooey and dark brown. Add a bit of white wine to deglaze the pan. 

Add apples and continue cooking until apples are soft and lightly browned. Add garlic, reduce heat and cook until the mixture has pulled together. Season with salt and pepper. Cool completely.

Preheat oven to 500°F. Generously grease an 18 x 13 inch pan or 2 smaller pans with oil.

Roll out dough, lightly stretching it to fit the pan. Transfer to the pan and pull to the edges. Create a small border by pinching the edges. Dimple the surface of the dough with your fingertips to create small ridges and valleys. 

Distribute the onion mixture over the top. Add cheese, if using, and bake for 20-25 minutes until browned and bubbly.