Combine raspberries, sugar, and lemon zest in a medium pot. Bring mixture to a simmer over medium heat, stirring frequency. Simmer until thick and jammy, about 8-10 minutes. It should coat the back of a spoon. Remove compote from heat and pour into a shallow bowl. 

Cool for 10 min at room temperature and transfer to the freezer to cool faster. Stir every 5-10 minutes until fully chilled (you can do this while preparing dough).

In a large mixing bowl, whisk together the flour, sugar, and salt. Cut cold butter into small cubes and add to the bowl. Use your fingertips or a pastry cutter to cut butter into the flour until incorporated (butter should be about pea-sized).

Slowly drizzle in cold milk and stir until a soft dough forms. You may need to get in with your hands to fully incorporate the milk. The dough should easily come together and not feel sticky.

Transfer the dough to a lightly floured surface. Form into a rough mound and divide in half. Flatten each half into a 1" thick disc and tightly wrap with plastic wrap. Refrigerate dough for at least 1 hour.

Line a large baking sheet with parchment paper. Remove the dough from the fridge. Transfer to a lightly floured surface. Place 1 sheet of parchment paper on top of the dough. Roll the dough out to an 8×6.5" rectangle. Cut off any rough edges. Cut into four, equal-sized small rectangles. Transfer the small rectangles to the prepared baking sheet. Transfer to the fridge.

Repeat previous step with remaining dough disc. To half of the small rectangles, place 2 tbsp of filling into the center. Brush egg wash or non-dairy milk along the edges. Place another rectangle on top of the one with filling. Seal the strudel by crimping the edges with a fork. Pierce the center of each sealed strudel with a fork.

Transfer sealed strudels to the fridge and refrigerate for 15 minutes.

Preheat the oven to 350°F. Before baking, brush each strudel with egg wash or non-dairy milk. Sprinkle over raw/turbinado sugar. Bake toaster strudels for 30-33 minutes until golden brown. Cool for 15 minutes on the baking sheet before transferring to a wire cooling rack.

While toaster strudels are cooling, prepare the icing. Whisk together all ingredients in a medium-sized mixing bowl until creamy. Drizzle icing over the toaster strudels and garnish with fresh raspberries.