Soak dried mushrooms in boiling water until they are soft and flexible (at least 2 hours).
Pat the beef dry with paper towel and sprinkle on all sides with salt and pepper.
In a heavy skillet, heat the oil until it is very hot, but not smoking, and brown the beef, turning it often so it browns evenly on all sides and doesn't burn (about 15 minutes).
Transfer the meat to a large casserole dish.
Bring broth and tomato paste to a boil over high heat in the skillet, stirring constantly (scraping the bottom and sides of the pan).
Pour the broth over the meat, cover tightly, and let simmer for 2 hours.
Place the mushrooms in a 1-qt saucepan with their soaking water and bring to a boil over high heat; reduce to low heat and let simmer, uncovered for 30 minutes.
Strain the mushrooms, reserving the liquid in a separate bowl.
Finely chop the mushrooms.
In a small pan, melt the butter and sauté the onions and garlic over medium heat until the onions are translucent, but not browned (2-3 minutes).
Add the mushrooms and cook for another 2-3 minutes.
Remove mixture from heat and let cool to room temperature.
Stir in bread crumbs, egg, salt, thyme, pepper, and parsley.
Moisten with 1 tablespoon reserved water from mushrooms.
When the meat has been braised, remove it from the casserole dish and with a very sharp knife slice it crosswise into 12 thin slices (slice to within an inch of the bottom, but do NOT slice all the way through).
Divide the stuffing into 6 equal portions and spread a portion on every other slice of meat, spreading as evenly as possible.
Slide 2 pieces of string under the beef criss-crossing them in the middle; bring them over the top and knot them securely to hold the slices in place.
Return the beef to the casserole dish and top with remaining reserved water from the mushrooms.
Bring to a boil over high heat; reduce to low, and let simmer until meat is tender (about 45 minutes).
Remove beef from pan and cover with foil to keep warm while you prepare the sauce.
Skim off and discard as much of the fat as possible from the liquid remaining in the casserole dish.
Return to a boil over medium heat.
In a small bowl, beat together all of the ingredients listed under sauce.
Beat about 1/2 cup of the hot stock into the sour cream mixture, and slowly pour back into the casserole dish.
Let simmer, stirring constantly until sauce thickens slightly (2-3 minutes) (Do NOT let it come to a boil or it may curdle).
Remove the strings and cut through every other slice of beef so that each serving consists of two slices of meat with stuffing in between.