Make the filling: Put the cookies in a food processor fitted with a metal blade and process them to crumbs.

Pour 1 to 2 inches of water into the bottom of a small saucepan and choose a bowl that fits over the saucepan to make a double boiler. Bring the water to a boil over high heat, then reduce the heat to medium-low.

Add the milk chocolate, bittersweet chocolate, and butter to the bowl of the double boiler and heat until they melt, stirring occasionally.

Remove the bowl from the double boiler and add the cookie crumbs and honey, and stir to combine. Set the filling aside to cool slightly.

Remove the dough from the refrigerator. Roll the dough out into a 16-inch square.

Spread two-thirds of one portion of the filling evenly over the surface of the dough. Gently roll the dough away from you to form a fat roll.

Cut the roll in half through the middle so you have 2 rolls, each approximately 10 inches long.

Spread the remaining portion of filling across the top of one of the 2 halves and place the second half on top to form an X. Twist the ends of the bottom roll up and over the top roll.

Place the babka into a prepared loaf pan. Repeat with the second babka.

Cover each babka and set it in a warm place to proof for 2 to 3 hours.

Preheat the oven to 350°F.

Whisk the egg with the salt to make an egg wash. Brush the wash over the babka surfaces.

Bake for 45 to 50 minutes until deep golden brown.

Make the glaze: Use a double boiler to melt the milk chocolate, bittersweet chocolate, butter, and honey.

Spoon the warm glaze over the babkas while they are still warm. Wait for the glaze to set before slicing.