Make the focaccia pizza dough

1. Combine yeast and sugar in a small bowl. Add warm water and let sit 10–15 minutes until foamy.
2. Place flour in a large bowl. Add the yeast mixture and stir until the dough comes together, adding water one tablespoon at a time if needed. The dough should be soft but not sticky.
3. Turn onto a lightly floured surface and knead for 1–2 minutes. Form into a ball.
4. Place in an oiled bowl, coat the top lightly with oil, and cover. Let rise until doubled in size, about 45–60 minutes.
5. Punch down, knead briefly, and shape on a baking sheet.

Make the balsamic glaze

1. Combine the balsamic vinegar and brown sugar in a small saucepan over medium heat. Bring to a gentle simmer and cook for 6–10 minutes, or until reduced by about half and lightly syrupy — it should coat the back of a spoon but still flow.
2. Remove from the heat and let cool; it will continue to thicken as it stands.

Assemble and bake

1. Preheat oven to 425°F.
2. Brush dough with olive oil and sprinkle with salt. Dimple the surface with your fingertips.
3. Top evenly with apple, red onion, vegan cheese, and olives. Brush exposed edges lightly with olive oil.
4. Bake 10 minutes, until edges begin turning golden.
5. Remove from oven, add walnuts and thyme, and bake 2–3 minutes more.
6. Drizzle with balsamic glaze and serve immediately.