French Dip Sandwiches

Serves 4

1/2 to 3/4 pound leftover meat from a beef roast
1 can beef broth
3 sprigs fresh thyme
4 deli submarine rolls
4 ounces Gruyère (or Swiss) cheese, shredded
4 tablespoons mayonnaise

Place the leftover beef wrapped tightly in plastic wrap in the freezer for 20 minutes.  Meanwhile, pour beef broth into a medium saucepan and add the sprigs of thyme.  Bring to a boil, then reduce heat to low and simmer until the beef is done freezing.  Remove the beef from the freezer and slice as thinly as you can get it (you can send it through the thin slicing disc of a food processor if you've got one).  Remove the thyme from the beef broth and add in the thin-sliced meat.  Let it simmer for 2-3 minutes just until meat is heated through.  Meanwhile, turn the broiler to "high" and set the oven rack on the second-to-highest rack.  Slice the sub rolls in half and spread the top half of each with 1 tablespoon mayonnaise.  Divide the cheese evenly over the top of the mayonnaise.  Pour the contents of the saucepan with the beef and broth through a fine mesh strainer so the broth goes into a serving bowl.  Place the meat into a second bowl.  Pour the broth into 4 small ramekins or serving bowls.  Divide the meat evenly on the second side of each roll, then place the sandwiches open-face on a large baking sheet and broil until the cheese is melted and edges of sandwich look golden and toasted, about 2-5 minutes.  Remove the sandwiches from the oven, put the halves together and serve immediately with jus on the side.

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