The core of the recipe is the combination of bite-sized pan-fried pieces of high-quality beef with sour creme and pickled cucumber. This may sound weird, but is actually a very satisfying combination.
My inspiration for this particular version comes from the (German language) cooking book Die russisch-baltische Küche, which lists a number of different variants. However, I mostly developed this following my own feeling and reverse-engineering a number of good Boeuf Stroganoff's I have eaten over time.
After these preparations, cooking will take about 15 minutes. Keeping the finished Boeuf hot is a bad idea - the meat is bound to overcook and get tough. Hence now is the time to start the side dishes. Suitable are pasta (very good for a first try - it allows you to concentrate on the main dish), boiled potatos, or, most classical, fried potatoes. I like my own rosemary fried potatoes (German link).
To continue the boeuf: Fry half the diced onions on medium high in butter until they are lighly browned. Add the garlic and keep striring for 20 seconds. Then add the mushrooms and 1/2 cup of water. Reduce heat to low medium and cook, covered, for 3 minutes. Then reduce heat to low. Blend the sweet and the sour cream with a table spoon each of mustard and tomato puree, and add it to the mushrooms. Season with salt and pepper, then let it simmer on the lowest heat setting.
In a second frying pan, heat up a few table spoons of oil and quickly sear the beef on high heat. After about one minute, add the remaining onions, and season with salt and pepper. Keep stiring for another minute or so. The beef should be browned on the outside, but still slightly bloody on the inside (if you want it well done, go to alt.cooking.how.to.spoil.food for instructions). Deglace the pan with a very small amount of water (i.e. add a few table spoons of water and keep stiring to free the tasty bits of caramelized meet and onions that stick to the pan - they give taste to the sauce).
Now add together diced cucumber, meat, and mushroom sauce. Add the lemon juice, mix, and season to taste. Let the ragout simmer for two minutes, then serve soon.