31/2 Tbsp unsalted butter (salted is fine)
1 Tbsp all purpose flour
1 C beef broth or stock
1 lb beef tenderloin or fillet mignon sliced 1/4" thick and cut into 1 inch pieces
salt and pepper to taste
2 Tbsp olive oil
1/2 C thinly sliced shallots (or regular onions)
3/4 lbs mushrooms halved or quartered depending on size
3 Tbsp sour cream (or more to taste), at room temperature
1 tsp Dijon mustard
2 Tbsp chopped fresh dill (optional) or use dried dill
Melt 1 1/2 Tbsp butter in a 1 quart heavy sauce pan. Whisk in the flour and cook whisking constantly for 2 minutes to make a roux. Add the stock in a slow steam, whisking constantly and bring to a boil. Reduce heat and simmer, whisking occasionally for 3 minutes. Remove from heat and cover to keep warm.
Pat beef dry and season well with salt and pepper. Heat 1 Tbsp butter and 1 Tbsp oil over moderately high heat until foam subsides. Add the beef in 2 batches and cook, turning once until browned on both sides but still pink inside, about 1 minute per batch. Transfer to a plate.
Add remaining 1 Tbsp each oil and butter to the skillet and heat until hot but not smoking. Add shallots and cook stirring occasionally until golden brown, about 3 minutes. Add the mushrooms and cook until the liquid from the mushrooms have evaporated and are browned, about 8-10 minutes.
Return meat with its juices to skillet and stir to combine, then transfer to a platter.
Reheat the sauce over low heat, the whisk in the sour cream, mustard, dill, 1/2 tsp salt and 1/4 tsp pepper (do not let boil). Pour sauce over beef and serve with buttered noodles.