Combine the water, sourdough starter, and raw honey in the bowl of a stand mixer fitted with the dough hook. Pulse the mixer a few times just to distribute the starter; it does not need to be completely dissolved.

Add the bread flour and coarse sea salt. Knead on low speed for 5 to 7 minutes. The dough will be sticky and rough but should gradually pull away from the sides of the bowl and cling to the hook.

Cover the mixer bowl and set it aside at room temperature for 30 minutes.

Remove the cover and perform one round of stretch and folds. Grab one side of the dough, lift it up and over itself, then rotate the bowl 90 degrees and repeat three more times. Cover the bowl again and rest for 30 minutes.

Repeat the stretch-and-fold process until you have completed three total sets with a 30 minute rest after each. After the last fold, use a little of the softened butter to grease a large clean bowl, transfer the dough into it, and cover for bulk fermentation.

Place the covered bowl in a warm spot and let the dough ferment until it has nearly doubled in size, about 3 to 4 hours depending on the temperature of your kitchen. While the dough ferments, prepare the apple fritter filling.

Melt the butter in a small saucepan over medium low heat. Whisk in the granulated sugar and bread flour, then cook until the mixture thickens into a smooth paste, stirring constantly.

Peel and dice the apple. Add the apple, brown sugar, cinnamon, and coarse sea salt to the saucepan. Cook over medium low heat, stirring often, until the apples soften and the mixture thickens. Remove from the heat and cool completely at room temperature.

When the dough has finished bulk fermenting, melt the remaining butter if it has solidified. Pour 2 tablespoons of the melted butter into a greased 9 by 13 inch baking pan and drizzle 1 tablespoon over the dough.

Use a bowl scraper to turn the dough out into the buttered pan. Gently press it into a rough rectangle to cover most of the pan. Spread half of the cooled apple filling over the surface.

Fold in the four sides, long sides first and then short sides, to create a rectangular package. Flip the dough seam side down, then spread the rest of the filling on top. Cover the pan with plastic wrap and let it proof until nearly doubled, about 2 to 3 hours. At this point you can bake immediately or cold retard the pan in the refrigerator for up to 2 days.

Melt the last tablespoon of butter. Use a little to oil your fingers and drizzle the rest over the shaped dough. Gently dimple the surface all over with your fingertips, pressing down and wiggling slightly; stretch the dough as needed to fill the pan.

Preheat the oven to 425 degrees F while the pan rests. Once the oven is hot, bake the focaccia for 25 to 30 minutes until deep golden brown. The internal temperature should be about 200 degrees F on an instant-read thermometer.

Cool the focaccia in the pan for at least 10 minutes, then transfer to a wire rack. While it cools, whisk the powdered sugar, milk, vanilla paste, and pinch of salt in a small bowl to make the glaze.

Drizzle the glaze evenly over the warm focaccia and serve.