Toast the sourdough for 3–4 minutes until deeply golden but not burnt.
Butter the toast with salted butter and spread raspberry conserve while still warm.
Pulse the toast in a food processor until you have small flakes and chunks.
Weigh out 60g of the toast flakes into a separate bowl and set aside.
Melt the 80g unsalted butter over medium heat to make brown butter.
In a stand mixer, mix cold cubed butter, cooled brown butter, miso paste, granulated sugar, and muscavado sugar until creamy.
Add the egg, egg yolk, and vanilla, mixing until fully incorporated.
In a separate bowl, whisk together flour, baking soda, baking powder, and salt.
Add dry ingredients to wet mixture and mix until just combined.
Fold through the white chocolate chunks and the reserved toast flakes.
Spoon raspberry conserve over the surface of the dough for visible marbling.
Portion the dough into large balls and roll in remaining toast flakes.
Refrigerate for at least 1 hour, ideally 12-30 hours.
Preheat the oven to 190°C and arrange cookies on a lined baking tray.
Bake for 9–11 minutes until golden brown at the edges.
Press reserved white chocolate chunks into the tops of the cookies while still hot.
Allow cookies to cool on the tray for 5–10 minutes before transferring to a rack.
