Preheat oven to 350 degrees F.

Season short ribs with salt and pepper. Heat olive oil in a Dutch oven or oven-safe large pot over medium-high heat. When the oil is smoking hot, add the short ribs and sear on all sides until browned and caramelized. Remove from heat and transfer to a baking dish.

Reduce heat to medium. Add onions, carrots, and celery to the same pot and saute until softened and translucent about 5 minutes. Add garlic and saute another minute. Add tomato paste and stir to coat the vegetables in the paste. Add red wine and bring to a boil. Add back the short ribs along with the chicken broth, canned tomatoes, bay leaves, oregano, thyme, and crushed red pepper flakes. Cover the pot and bake in the oven until short ribs are tender, about 3 hours.

Meanwhile, prepare the gnocchi. Combine goat cheese, eggs, salt and pepper in a bowl of a stand mixer. Beat just until combined. Add the flour and beat until a soft dough begins to form, adding additional flour 1 tablespoon at a time if needed. Portion the dough into 4 pieces. Wrap in plastic wrap and chill for 30 minutes.

Remove one portion of the dough from the fridge. Dust a clean work counter with flour and roll out the dough into a 1-inch thick rope. Cut the rope into ¾-inch pieces. Transfer the gnocchi onto a lightly floured baking sheet and repeat with the remaining dough.

Remove short ribs from the oven when can easily be shredded with a fork. Transfer the short ribs onto a plate and pour the braising liquid as well as the cooked vegetables into a blender. Blend until smooth. Pour the sauce back into the pot and season with salt and pepper. Simmer the sauce until slightly reduced, about 5 minutes. Return the short ribs to the sauce and keep warm.

Bring a large pot of salted water to a boil over medium-high heat. Add the gnocchi in batches and cook until they start to float to the top about 1-2 minutes. Remove gnocchi with a slotted spoon directly into the sugo. Gently toss to combine and portion into 4 bowls. Finish with grated parmesan on top. Serve immediately.