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 softened cream cheese in a medium bowl until smooth. Add sugar, vanilla extract, and lemon juice. Mix until creamy and fully combined. Set aside until ready to use.
03 - Combine raspberries, sugar, cornstarch, and lemon juice in a small saucepan. Cook over medium heat, stirring constantly, until mixture thickens, about 3 to 5 minutes. Remove from heat and allow to cool completely.
04 - Preheat oven to 375°F. Line a baking sheet with parchment paper. On a lightly floured surface, roll chilled dough to 1/4-inch thickness. Cut into 8 rectangles or circles and place 2 inches apart on prepared baking sheet. Create an indentation in center of each piece using fingers or spoon back. Spoon 1 tablespoon cream cheese filling into each center, then top with raspberry filling.
05 - Let assembled pastries rest at room temperature for 20 to 30 minutes until slightly puffed. Brush edges lightly with beaten egg. Bake for 20 to 25 minutes until golden brown and set. Transfer to wire rack to cool completely.
06 - Whisk together powdered sugar, milk or cream, and vanilla extract until smooth. Drizzle glaze over cooled danishes before serving.