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Ingredients
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Sandwich
Gravy
Optional garnish & sides
Method
Make the gravy
Warm liquids
Place the 3 cups of broth and 1/2 cup pan drippings or extra stock in a medium saucepan and warm over medium heat until gently simmering. Keeping the liquid warm helps the roux incorporate without lumps.
Make roux
In a separate heavy-bottomed skillet or saucepan, melt 3 tablespoons butter over medium heat. Sprinkle in the 3 tablespoons all-purpose flour and whisk constantly for 2–3 minutes until the mixture turns a light golden tan and loses the raw flour smell. Do not let it brown too dark if you want a lighter gravy; for richer color allow it to deepen slightly.
Combine and thicken
Slowly whisk the warm broth mixture into the roux in a steady stream, whisking constantly to maintain a smooth gravy. Bring to a gentle simmer; the gravy will thicken as it heats. Simmer for 4–6 minutes, whisking occasionally, until it reaches a saucy consistency that coats the back of a spoon.
Season gravy
Stir in 1 teaspoon Worcestershire sauce, 1 teaspoon soy sauce (if using), 1/2 teaspoon salt, and 1/2 teaspoon freshly ground black pepper. Taste and adjust seasoning as needed. If gravy becomes too thick, whisk in a tablespoon or two of hot broth until desired consistency is reached.
Prepare meat and bread
If using leftover roast, thinly slice or shred the meat into bite-sized pieces. If using deli slices, separate and lay them out so they will heat evenly. Place the meat in a shallow baking dish or oven-safe skillet.
Preheat oven to 325°F (160°C). Heat the sliced meat in the oven for 8–12 minutes until warmed through, or warm in the microwave in 30-second intervals until hot. If you prefer, briefly simmer the meat in 1/2 cup of the prepared gravy on the stovetop to warm and flavor it (use low heat and do not overcook).
Lightly butter one side of each bread slice or roll interior with softened butter. For open-faced style: arrange 1/2 cup warmed meat on each slice of bread (about 2 slices per sandwich) and place on a baking sheet. For closed sandwiches: assemble the meat between two slices, buttered sides out, and wrap in foil.
Assemble and finish
For open-faced sandwiches: ladle hot gravy generously over each assembled open sandwich so gravy soaks into the bread and covers the meat. Place the baking sheet under a broiler for 1–2 minutes just to warm the top (watch closely). For closed sandwiches: place wrapped sandwiches in the preheated oven for 6–8 minutes to melt slightly and warm through; serve with gravy on the side for dipping.
Transfer sandwiches to plates. Spoon any remaining gravy over the sandwich (open-faced) or serve in a small bowl alongside for dipping (closed). Garnish with chopped parsley and add pickles on the side if desired.
Serve immediately while hot. Leftover gravy can be refrigerated up to 3 days and reheated gently, thinning with a little broth if necessary.