In a large mixing bowl, combine the active sourdough starter with warm water. Stir until the starter is mostly dissolved.

Add the flour and salt to the bowl. Mix with a spoon or your hands until a shaggy dough forms and no dry streaks of flour remain. Cover the bowl with a lid or plastic wrap and let it rest for 30 minutes (autolyse).

After the rest, pour 2 tablespoons of olive oil over the dough. Using wet hands, perform a series of stretch and folds: grab a portion of the dough, stretch it upwards, and fold it over itself. Rotate the bowl and repeat until you've gone around the entire dough (about 4-6 folds). Repeat this process every 30 minutes for 3-4 rounds, covering the dough between each round.

After the final stretch and fold, cover the bowl and let the dough bulk ferment at room temperature for another 2-4 hours, or until it has visibly increased in volume by about 20-30% and looks airy. (Alternatively, you can place it in the refrigerator for an overnight cold proof, 8-12 hours, after bulk ferment for deeper flavor).

While the dough is doing its final bulk ferment (or after removing from cold proof), prepare the apple topping. In a small saucepan, melt the butter over medium heat. Add the diced apples, brown sugar, cinnamon, and nutmeg.

Cook, stirring occasionally, for 5-7 minutes until the apples have softened slightly and the sauce has thickened. Stir in the 1 tablespoon of all-purpose flour to help bind the mixture. Remove from heat and let cool completely.

Lightly grease a 9x13 inch baking pan generously with olive oil. Gently transfer the dough to the prepared pan. Pour a tablespoon of olive oil over the dough and gently spread it out to fill the pan, being careful not to degas it too much. If the dough springs back, let it rest for 10 minutes, then continue stretching.

Cover the pan with plastic wrap or a clean kitchen towel and let it proof in a warm spot for 1-2 hours, or until it looks puffy and airy. Towards the end of the proofing, preheat your oven to 425°F (220°C).

Once the dough is fully proofed, drizzle with a little more olive oil. Gently press your fingertips into the dough to create dimples. Spoon the cooled apple fritter topping evenly over the surface of the focaccia, gently pressing some into the dimples.

Bake for 25-30 minutes, or until the focaccia is golden brown on the edges and cooked through. If the apples start to brown too quickly, you can loosely tent with foil.

Remove the focaccia from the oven and let it cool in the pan for 5-10 minutes before carefully transferring it to a wire rack to cool completely.

In a small bowl, whisk together the sifted powdered sugar, 2 tablespoons of milk or cream, and vanilla extract until smooth. Add more milk/cream a teaspoon at a time if needed, to reach a pourable but thick consistency.

Once the focaccia is completely cool, drizzle the vanilla glaze generously over the top. Let the glaze set for a few minutes before slicing and serving.