Add 1 tablespoon of cooking oil to a Dutch Oven, or pot, and heat on medium heat until shimmering, then add chopped onions. Cook until onions begin to brown and add mushrooms. Continue to saute until mushrooms are tender and onions have browned. Add minced garlic and cook 1 minute longer, or until fragrant.
Remove onions, mushrooms, and garlic into a separate bowl and set aside. Deglaze the bottom of the pot with ~1/4 cup of beef broth, scraping the bottom of the pot to remove the burnt on fond as the liquid boils. Pour off liquid into bowl with onions, mushrooms, and garlic.
Add 2 tablespoons of cooking oil to the pot set to high heat. Sprinkle salt over beef cubes and add them to the heated oil to brown on all sides. For best browning, refrain from stirring the meat, except when needed to turn the beef for even browning.
Once beef is browned on all sides add the remaining 3 3/4 cups of beef broth to the pot along with the onions, mushrooms, garlic and deglazing liquid that was set aside. Also add Worcestershire sauce, Soy sauce, and Bay leaf to the pot, cover and bring to a simmer.
Simmer on low for 60 - 90 minutes, or until beef is tender (the longer it is cooked, the more tender it becomes)
Remove everything from the pot and pour through a strainer into a bowl to separate liquid.
Prepare the gravy in the Dutch Oven by melting 1/4 cup of butter into the pot set on medium low heat. Sprinkle flour over the melted butter and whisk continually for 4 minutes to prevent scorching.
Slowly add 2 cups of liquid to the flour mixture (roux) using any leftover liquid strained off from simmering the beef. If most of it evaporated add additional beef broth to equal 2 cups of liquid. Continue to whisk as liquid is added.
Gently cook the gravy until it begins to thicken, then add salt and pepper to taste along with a few drops of browning sauce.
Return beef and mushroom mixture to the pot and combine with the gravy.
Serve beef tips and gravy over a side of mashed potatoes or egg noodles.