Season the short ribs generously with kosher salt and black pepper. Heat a large skillet over high heat and sear the ribs on both sides until browned. Transfer the seared ribs to the slow cooker.
Into the slow cooker with the ribs, add the crushed San Marzano tomatoes, tomato paste, chopped oil-packed sun-dried tomatoes, red wine, carrots, chopped yellow onion, and pickled jalapeños. Season generously with Italian seasoning, additional salt, pepper, and chili flakes. Stir everything well to combine.
Place a parmesan rind into the sauce and add a whole head of garlic. Cover the slow cooker and cook on low for 7-8 hours or on high for 5-6 hours, until the short ribs are tender and falling off the bone. During the final hour of cooking, carefully remove the whole head of garlic.
Once removed, squeeze the softened garlic cloves out of their skins. In a small skillet, melt the butter over medium heat. Add the mashed garlic cloves to the butter, mashing them further. Allow the butter to brown slightly and some of the garlic to get crispy. Remove from heat.
Remove and discard the parmesan rind from the sauce. Shred the tender beef short ribs directly into the slow cooker, stirring them into the sauce. Stir in the garlic butter mixture until fully incorporated.
Serve the rich Sunday Sauce over your favorite pasta. Garnish with freshly grated parmesan cheese and fresh basil leaves. Enjoy this comforting meal!