Turn the risen dough out onto a lightly floured counter and divide it in half. Work with one piece of dough at a time; keep the other half loosely covered.
Roll out one piece of dough into a 10 x 16 inch rectangle. Spread half of the fig jam evenly over the surface, leaving a 1-inch border along the long edges. Layer half of the salami slices over the jam, overlapping slightly. Spread half the Dijon mustard over the salami slices.
Starting with the short edge closest to you, roll the dough into a tight log, pressing gently as you go. Use both hands to even out the roll into a perfect thick cigar. Place the rolled log on a parchment-lined baking sheet, seam side down, and transfer to the freezer for 10–15 minutes to firm up.
Repeat the rolling filling and freezing process with the second piece of dough, using the remaining fig jam, salami and mustard.
Working with one chilled log at a time, use a sharp knife to cut the log in half lengthwise. With the cut sides facing up, twist the two halves together to form a braid. Carefully transfer the twisted dough to a parchment-lined 8x4 inch loaf pan. Repeat the cutting, twisting, and shaping process with the second chilled log. Cover both pans loosely and let rise until puffy, about 45–60 minutes.
Preheat the oven to 350°F (180°C). Brush the tops of the loaves with beaten egg and sprinkle generously with Everything Bagel spice. Bake for 20 minutes minutes and check to see how quickly the top is browning. If it is getting too dark, cover loosely with foil until the loaves are deep golden brown and the internal temperature reaches 195°-200°F. (91°-93°C) Cool in the pans for 15 minutes, then transfer to a wire rack to cool completely before slicing.