01 - Cut cold butter into flour in a large bowl until mixture resembles coarse crumbs. Mix in sourdough discard, sugar, and salt until soft dough forms. Shape into a disk, wrap in plastic, and refrigerate for at least 1 hour.
02 - Beat cream cheese in medium bowl until smooth. Add sugar, vanilla, and lemon juice; mix until creamy and fully combined. Set aside at room temperature.
03 - Combine raspberries, sugar, cornstarch, and lemon juice in small saucepan. Cook over medium heat, stirring constantly, until thickened, 3–5 minutes. Remove from heat and let cool completely.
04 - Preheat oven to 375°F. Line baking sheet with parchment paper. On lightly floured surface, roll chilled dough to ¼-inch thickness. Cut into 8 rectangles or circles. Place 2 inches apart on prepared sheet. Create indentation in center of each piece. Spoon 1 tablespoon cream cheese filling into each center, then top with raspberry filling.
05 - Let assembled pastries rest at room temperature for 20–30 minutes to puff slightly. Brush edges lightly with beaten egg. Bake for 20–25 minutes until golden brown and set. Transfer to wire rack to cool completely.
06 - Whisk powdered sugar, milk, and vanilla until smooth and drizzling consistency. Drizzle over cooled danishes before serving.