Pulse the flour, 3 tablespoons of the granulated sugar, 1 teaspoon of the cinnamon, and 1/2 teaspoon of the salt in a food processor until combined. Add the butter and pulse until a few pea-size clumps of butter remain. Add the cream cheese and vanilla and pulse just until the dough forms a ball.
Divide the dough in half and place on 2 sheets of plastic wrap. Shape into 1 inch thick disks. Wrap and chill until completely firm, for 2 hours and up to 2 days.
Combine the walnuts, brown sugar, nutmeg, and the remaining 1/2 teaspoon of cinnamon and 1/4 teaspoon of salt in a small bowl. Set aside.
Working with one piece of dough at a time, roll on a floured surface into a 13-inch round. Top with 1/4 cup of the jam and sprinkle with half of the walnut mixture. Cut the round into 12 equal wedges, like pizza slices. Roll up each wedge, starting at the outer edge. Repeat with the remaining dough, jam and walnut mixture.
Place the rugelach 1 1/2 inches apart on 2 rimmed baking sheets lined with parchment. Brush with the egg and sprinkle with the remaining tablespoon of granulated sugar. Bake, rotating the sheets halfway through, until golden, 25 to 30 minutes. Transfer to a wire rack to cool completely.