First things first, heating a large skillet over medium-high heat is crucial. Add the olive oil, letting it get nice and hot. Season your beef short ribs generously with salt and pepper. Once the oil shimmers, place a few ribs in the pan, searing them on all sides until they develop a lovely brown crust. This step is vital because it locks in flavors and adds depth to the dish. Set the seared ribs aside on a plate.

In the same skillet, take advantage of the drippings in the pan. Add the roughly chopped onion, diced celery, and carrots. Sauté until the onions are translucent and fragrant, about 5 minutes. Toss in the smashed garlic cloves and stir for an additional minute.

Here’s the fun part! Pour in the red wine. Scrape the bottom of the pan with a wooden spoon, gathering all those flavorful browned bits. Let the wine simmer for about 2-3 minutes. This helps to reduce the acidity while enhancing the flavor profile.

Now, transfer the sautéed mixture into your slow cooker. It's time to add the tomato paste, Worcestershire sauce, smoked paprika, bay leaves, and beef broth. Stir everything together to create a delicious sauce that will coat the ribs.

Nestle the seared ribs into the slow cooker. Ensure they are mostly submerged in the flavorful liquid. You want every bite to be saturated with sauce.

Cover your slow cooker and set it on low for about 8 hours (or high for 4 hours if you're short on time). The slow cooking will work its magic as the meat becomes tender enough to fall off the bone.

Once cooked, carefully remove the ribs. Discard the bay leaves and adjust seasoning if required. You can thicken the sauce on the stove if it's too thin, or serve it as is. The swelling aromas will captivate everyone at the table.