Dice onion and grate garlic using a microplane. Place in a bowl. Add seasonings and stir to coat. Set aside.
Preheat oven to 325°. Preheat braiser or small dutch oven on the stovetop (medium heat).
Salt short ribs on all sides. Add a small amount of olive oil to the braiser or dutch oven. Sear all four long sides for 2 minutes per side. Transfer to a plate.
Saute onions and garlic until they begin to become caramelized.
Deglaze the pan with the red wine.
Return the short ribs to the pan, along with the beef stock. Depending on the size of the pan you’re using, you may not need all of the stock. The stock should come about halfway up the short ribs.
Move the pan to the oven and cook with the lid on for about 2 hours, until the meat easily shreds apart with a fork.
Cook for an additional 15-20 minutes uncovered, then remove from the oven and let the short ribs rest.
Once the ribs have rested for about 20 minutes, remove them from the pan and pull the meat apart with a fork. Set the meat aside in a bowl with lots of paper towels to absorb the excess fatty liquid. Stir a few times to make sure the meat won’t be greasy in the ravioli.
Follow Chef Anne's All Purpose Pasta Dough recipe instructions for the dough. (I make my pasta dough in my KitchenAid mixer using the dough hook instead of kneading it by hand.)
Separate dough into portions about a half cup in size. Cover unused dough with plastic wrap.
Roll out dough to #6 setting using pasta machine (start on the widest setting, #1, and work your way thinner).
Place pasta dough strips back onto floured work surface. Cover with plastic wrap until it’s time to use them.
Bring a pot of water to a boil while assembling the ravioli, and begin heating the sauce on the stovetop.
Scoop short ribs onto one half of each pasta sheet. You’ll want somewhere between 1 tsp to 1 tbsp of filling depending on the size of the ravioli. Be careful not to overfill because you want a good seal. Fold the other half of the sheet over. Press around each of the ravioli to seal tightly. Cut with a ravioli stamp or pastry wheel.
Boil the ravioli for about 7 minutes. To check for doneness, test an edge since this is the thickest part that takes longest to cook.
Remove the ravioli from the pot using a spider spoon. Toss the ravioli in the sauce on the stovetop. Transfer to a plate and top with grated parmesan.