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1
Melt 1 1/2 tablespoons butter in a small heavy saucepan over moderate heat and whisk in flour, then cook roux, whisking constantly, 2 minutes.
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2
Add broth in a slow stream, whisking constantly, and bring to a boil.
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3
Reduce heat and simmer, whisking occasionally, 3 minutes.
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4
Remove from heat and keep warm.
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5
Pat beef dry and season well with salt and pepper.
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6
Heat 1 tablespoon butter with 1 tablespoon oil in a 12-inch heavy skillet over moderately high heat until foam subsides.
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7
Saute beef in two batches, turning once, until browned on both sides but still pink inside, about 1 minute.
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8
Transfer to a plate with a slotted spoon.
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9
Heat remaining tablespoon butter with remaining tablespoon oil in same skillet over moderately high heat until hot but not smoking, then saute shallot, stirring occasionally, until golden brown, about 3 minutes.
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10
Add mushrooms and saute, stirring occasionally, until liquid mushrooms give off is evaporated and mushrooms are browned, about 8 to 10 minutes.
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11
Return meat with its juices to skillet and stir to combine, then transfer to a platter.
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12
Reheat sauce over low heat (do not let boil), then whisk in sour cream, mustard, dill, salt, and pepper.
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13
Pour sauce over beef and serve immediately.
