Dust the surface of the refrigerated dough with flour and divide in half. Dust the first piece with flour and shape into a rough ball by stretching the surface of the dough around to the bottom, rotating the ball a quarter-turn as you go.
Using a rolling pin, roll the first piece of dough out to a 1/4-inch-thick rectangle, about 9 x 12 inches. As you roll out the dough, add flour as needed to prevent sticking.
Transfer the dough onto the lined baking sheet. Place the cream cheese filled down the length of the dough in a 3-inch strip in the center, and add the jam on top in an even layer.
Using a sharp paring knife or a pair of kitchen scissors (I found the scissors to actually work best), cut about 1/2-inch-wide strips down each side. Twist and then fold the strips, left over right, crisscrossing over the filling. Lightly press the strips together you move down the pastry, creating a braid.
Repeat with the second braided loaf.
Cover loosely with plastic wrap and allow them to rest at room temperature for 60 minutes.
Preheat the oven to 350 degrees F, with a rack placed in the center of the oven.
Brush the braids lightly with egg wash. Bake the braided loaves for 30 to 35 minutes, or until golden brown. Allow to cool.