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