This may be a little more work than the average cookie, but these divine Apricot-Walnut rugelach are truly worth it.
In a food processor, process butter, cream cheese, 3 tablespoons sugar, and salt until combined. Add flour and pulse until a dough forms. Divide in half, flatten into disks, and tightly wrap in plastic. Refrigerate until firm, 2 hours (or overnight).
In a small pot, bring apricots, brandy, cinnamon, and 1/2 cup water to a boil. Reduce heat and simmer until most of liquid is absorbed, 7 minutes. Transfer to clean food processor. Pulse until finely chopped. Stir in walnuts and remaining 2/3 cup sugar.
Working with 1 disk at a time, on a floured surface, roll out dough into a 12-inch circle. Spread with half the filling, leaving a 1-inch border. Cut into 16 wedges. Starting from outside edge, tightly roll each wedge up; place on parchment-lined baking sheets, seam side down. Lightly brush with egg. Freeze 30 minutes.
Preheat oven to 325 degrees, with racks in upper and lower thirds. Bake until golden brown, 30 to 35 minutes, rotating halfway through. Transfer to wire racks; let cool completely.