Soak the raisins in warm water for 10 minutes to plump them up, then drain well and pat dry on paper towels. While they soak, measure out all your ingredients and have them ready—this is essential for cookie doughs that come together quickly. Preheat your oven to 170°C (340°F) so it's ready when you need it.
In a large bowl, combine the flour, sugar, mixed spice, and salt. Cut the butter into small cubes and add it to the dry mixture. Using your fingertips or a pastry cutter, work the butter into the flour until the mixture resembles coarse breadcrumbs—this creates a tender crumb structure in the final cookies. Fold in the drained raisins and mixed peel until they're evenly distributed throughout the dough. The dough should come together as a cohesive ball; if it feels too dry, add a few drops of water.
On a lightly floured surface, roll out the dough from Step 2 to about 1/2 cm (roughly 1/4 inch) thickness. Using a round cookie cutter or the rim of a glass, cut out circles and place them on a lined baking sheet, spacing them about 2 cm apart. In a small bowl, whisk together the egg white and 1.5 tbsp sugar until frothy. Brush the top of each cookie generously with this egg white mixture—this creates the glossy finish characteristic of hot cross buns.
Place the baking sheet in your preheated 170°C oven and bake for 8-10 minutes until the cookies are golden brown around the edges but still pale on top. I find that cookies baked at this lower temperature develop a better texture than those baked hotter—they stay tender inside while the outsides set properly. Remove from the oven and let cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
Once the cookies from Step 4 have cooled completely, melt the white chocolate (either in the microwave in 20-second bursts or over a double boiler, stirring frequently). Let it cool to room temperature so it's still pourable but not so hot it spreads uncontrollably. Transfer the melted white chocolate to a piping bag fitted with a small round tip or a squeeze bottle. Pipe a cross pattern on top of each cookie—two perpendicular lines that create the iconic hot cross bun design.