Season short ribs on all sides with salt and pepper.
Heat oil in a large skillet over medium-high heat.
Add seasoned ribs to the hot oil (bone side up first)and sear on each side for 1-2 minutes, until browned. (The ribs will not be cooked through.)
Remove and transfer ribs to a large crockpot.
To the same skillet, add onions, mushrooms, and tomato paste. Stir to coat the vegetables. Cook over medium heat until onions are tender (about 3-5 minutes).
Add garlic and cook for one more minute.
Increase the heat to high and pour in the beef cooking broth, stirring often and scraping up the brown bits from the pan. Bring the mixture to a boil and then reduce heat to medium. Simmer for 5 minutes, stirring and scraping the sides as needed.
Pour over the ribs in the crockpot.
Cover and cook on low for 7-8 hours. Or, cook on high for 3-5 hours.
The ribs are done cooking when they easily fall off the bone.
Serve over mashed potatoes.