Preheat oven to 325 degrees.
Pat short ribs dry with a paper towel and sprinkle lightly with salt and pepper.
Slice onions into ½ inch thick rings. Peel and slice carrots into 1 inch chunks on the bias. Mince garlic cloves. Set veggies aside.
Heat 2-3 tablespoons avocado oil in a large skillet, preferably cast iron, until screaming hot. Sear short ribs on all sides until brown crust forms. Do this in batches and transfer them to a large dutch oven as you go. This will take about 7-8 minutes.
Once the ribs are seared and in the dutch oven, lower the heat on the same skillet and add in the onions. Cooking down until they are browned, but not burned. About 6-8 minutes.
Add the minced garlic to the onions and cook for about another minute, until fragrant.
Add beer and crushed tomatoes to the skillet to deglaze the pan. Stir with a wooden spoon, scraping all of the brown bits from the bottom of the pan.
Add in the dijon mustard to the onion mixture and season with another pinch of salt and black pepper. Turn up the heat to medium. Stir and let simmer for 3-4 minutes, giving flavors time to meld. Taste for seasoning.
Place the raw carrot chunks on top of the seared short ribs in the dutch oven. Carefully pour the contents of the skillet over the short ribs and carrots into the dutch oven.
Bundle 5-6 sprigs of fresh thyme with twine. If you don't have any twine, I use a few extra tough thyme stems to tie it together in several places! Place thyme bundle on top and put the lid on the dutch oven.
Bake covered with the lid in the oven for 2 ½ to 3 hours until the meat is just barely clinging to the bone. Turn the ribs in the sauce with tongs about halfway through cooking.
Remove bundled thyme from the pot and discard.
Serve the short ribs on a bed of garlic mashed potatoes or creamy parmesan polenta.