In a stand mixer, cream together the butter, cream cheese, brown sugar, 2 Tbsp. of white sugar and salt. Mix in the vanilla, then the flour. Wrap dough in plastic wrap and chill 1 hour.
Preheat oven to 350 degrees. In a small bowl, combine the cinnamon and 2 tsp. of sugar. Set aside. Line 2 baking sheets with parchment paper.
Melt the chocolate in a microwave safe bowl in 20 second intervals until it is smooth. (Alternatively, melt the chocolate on the stove in a double boiler.) Stir in the sugar and salt. The mixture should be grainy.
Remove the dough from the refrigerator and divide it into 6 equal pieces. Form each piece into a ball using your hands.
On a floured surface, use a rolling pin to roll dough into a circle that is 1/4-inch thick. Spread the chocolate filling in the center of the circle, leaving a 2-3 inch perimeter of cookie dough around.
Using a pizza cutter or sharp knife, cut the dough circle into 10 wedges. Starting at the wide end of each wedge, roll the dough tightly towards the tip.
Place cookies, seam side down, onto a prepared baking sheet.
Beat the egg with 1 Tbsp. of water in a small bowl. Lightly brush the top of the dough with egg wash. Sprinkle with the cinnamon-sugar mixture.
Bake 18-20 minutes, until golden brown. Cool on the baking sheet for 10 minutes before transferring to a wire rack.