In a large pot, heat your butter, then as it foams add your onions and garlic.
Brown the onions/garlic. Add your spices.
Now add your short ribs browning each side.
Once the short ribs are browned on each side, add your tomatoes, carrots, and water/broth.
Cook on a low heat with the cover lid on for 2 to 3 hours. If you have bone in short ribs, the bones will fall out just fish them out at the end. You want to leave them in as you cook so they add flavor to the meal.
Once the short ribs are fully cooked (they should be so tender than they can break apart with your fork pretty much), remove them from the pot.
The short ribs tend to leave a lot of grease in a braising sauce, use a spoon remove all the excess fat as it will ruin the meal. I save the fat for later use down the road, it's perfectly fine.
Now add the gochujang, fish sauce, tomato paste, brown sugar, and rice wine to the pot. Stir intermittently for a 2 minutes on medium heat.
Use an immersion blender to completley puree the sauce, if you don't have one a regular blender will do, just be careful to not burn yourself.
Once it's completely smooth, add it back to your pot and allow it to simmer for 10 minutes.
While your sauce simmers, add your short ribs to a skillet and broil them in the oven for 1 minute on high to brown the tops. Be careful not to burn the meat.
Once it's all done, you can opt to cut the layer of fat off the back of the rib before you serve it.
Serve with your sauce and enjoy!