Position an oven rack in the center of the oven and preheat to 375 degrees F.
Wrap the sliced pastrami in foil and put on to a baking sheet. Remove 1/4 inch of the crust from the ends of the loaf, then cut the loaf crosswise into 4 even pieces. Use a fork to score one cut end and gently dig a square hole into each piece of bread to make a box, leaving a 1/2-inch layer of bread around the walls and bottom (see Cook's Note). Save the removed crumbs for another use.
Microwave the butter and a large pinch of salt in a small microwave-safe bowl until melted, about 1 minute. Brush the bread boxes inside and out with the melted butter. Put 1 slice of cheese at the bottom of each bread box. Put the boxes open-side up on the same baking sheet as the pastrami and bake until the cheese melts and the inside of the bread is lightly browned and crispy in parts, about 10 minutes. The pastrami should be warmed through.
Meanwhile, whisk together the mayonnaise, ketchup, horseradish, onion powder, Worcestershire sauce and hot sauce in a small bowl. Season to taste with salt if needed. Set aside.
Layer each bread box with 1 1/2 tablespoons of the dressing, a quarter of the pastrami, a quarter of the sauerkraut and top with 2 more slices of cheese. Return to the oven and bake until the cheese melts, about 5 minutes. Drizzle with the remaining dressing. Serve whole or cut in half.
Don't worry if you accidentally make a hole at the bottom of the bread when carving out the boxes--just fill the hole with a loose piece of bread.
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