Trim the bread into a cylinder with a large serrated bread knife, flattening out the top and evening out the sides so that you are left with a tall cake-like shape. (For neat edges, use a 6-inch cake pan or a small plate on top of the loaf as a guide to cut around.) Cut the bread horizontally into 4 layers, using a sawing motion.
Place the bottom bread layer on a serving plate or cake stand and cover with half of the mayonnaise. Layer on one container of the Black Forest ham. Place the second bread layer on top, cover with half of the mustard and top with the smoked turkey. Place the third bread layer on top, cover with the remaining mayonnaise and top with the remaining ham. Spread the cut side of the fourth bread layer with the remaining mustard and close the sandwich. Press down to adhere the layers together.
Frost the loaf with the cream cheese using an offset spatula. Press the scallions along the bottom edge of the loaf. Sprinkle the chives on the outer top edge of the loaf. Sprinkle the spring mix greens in the center of the cake. Arrange the cherry tomatoes cut-side down at regular intervals around the top of the cake. Serve immediately or chill until ready to serve.