In a large bowl, stir together warm water, yeast and sugar. Let it sit for about 10 to 15 minutes so the yeast can activate and turn foamy. While you wait you can already chop the apples into small pieces and place them in a bowl.
Next, add the flour, salt, lemon zest and olive oil. Mix everything together until it turns into a sticky dough. Let it rest for about an hour.
After the dough has risen, fold it by gently lifting one side, stretching it up and fold it over toward the center. Turn the bowl and repeat on other sides. After folding, let it rest again for at least another 30 minutes. If you have the time, you can also repeat that process multiple times, for a more fluffy dough.
The next step is to prepare the apple-cinnamon topping. Melt the vegan butter in a pan, then stir in the sugar for about a minute until it melts. After that add chopped apples, cinnamon, walnuts, and lemon juice. Sprinkle in a pinch of salt. Let everything sizzle for a few minutes until the apples soften. Set it aside to cool off.
Grease your baking pan with olive oil or vegan butter. Transfer the risen dough into the pan and gently stretch it to fit. Spread half of the apple topping over one half of the dough, then fold it so the apples are covered. Place the folded dough sideways in the pan. Let it rise again for 20 minutes until it puffs up nicely. Then spread the remaining apple mixture on top and gently press it into the surface with your fingertips.Once preheated to 180°/360F, bake the focaccia for about 25 minutes, until golden and caramelised on top. Mix together the powdered sugar with the plant milk. Stir until smooth and thick enough to drizzle over the focaccia and drizzle it over the bread. It will dry quickly and form that lovely white, crackly glaze. Then slice it up and enjoy!