Start by patting the pieces of beef dry using paper towels.
Season the dried pieces of beef with salt and pepper. I like to season it generously, but this is my personal preference.
Heat oil and butter over medium heat in a large, heavy bottomed sauce pot.
Once hot, sear the pieces of beef in batches (don't crowd the meat, or it will not brown as nicely). Cook until all sides are browned, approximately three minutes per side. Add more oil if needed. Transfer cooked pieces to a plate and continue until all pieces have been browned on all sides. Reserve the cooked pieces on the plate.
Add the mushrooms to the pot and stir. Deglaze, if needed, with a couple of splashes of broth. Cook the mushrooms, stirring every minute for about 10 minutes, until golden.
Add in the chopped onions, carrots, and celery. Season with salt and pepper, and stir. Cook for 5 minutes, stirring every minute.
Add minced garlic and stir for 1 minute.
Add the tomato paste and stir to coat all of the veggies.
Add the cooked beef back into the post, along with the beef broth, dried rosemary, and thyme, and stir well.
Bring the pot to a boil, then lower to medium-low. Let the stew simmer for a minimum of 1 hour (2-3 hours is better).
Serve warm.