Make challah dough as directed. Dust the surface of the refrigerated dough with flour and cut off three 6-ounce pieces (about the size of a small orange). Dust with more flour and quickly shape them into balls by stretching the surface of the dough around to the bottom, rotating the ball a quarter-turn as you go. Cover and allow the dough to rest for about 15 minutes.
Roll out the dough balls into rounds about 8-inch wide. As you roll out the dough, add flour as needed to prevent sticking.
Place one of the dough rounds on a piece of parchment paper. Top with 1/2 the soft cream cheese. Repeat with next layer of dough and the remaining cream cheese. Top with the final layer of dough.
Place a 2½-inch biscuit cutter or anything that size and round in the center of the dough. Use a pizza cutter or bench scraper to cut 16 equal spokes from the edge of the biscuit cutter to the outer edge of the dough.
Brush with egg wash and sprinkle on the everything bagel topping.
Twist two of the sections away from each other with two rotations, then pinch the two sections together at the end to form a point. Continue with the rest of the sections until you have 8 point.
Loosely cover the star and rest for about 90 minutes (60 minutes if using fresh dough that has not been refrigerated).
Preheat oven to 375°F. Brush the exposed dough with egg wash.
Bake for 20-25 minutes until golden and set. Allow to cool on a rack.