Preheat oven to 350°F. Generously season short ribs all over with salt and pepper.
Heat 2 tablespoons of olive oil in a large Dutch oven over medium-high heat. Add ribs in two batches (four per), browning each side for about 1 minute (flip four times). Place on a plate and set aside.
Reduce heat to medium and add onions, carrots, and garlic. Cook for 2 minutes. Add tomato paste and flour, stirring to coat. Add red wine and deglaze the pan. Bring to a boil and cook for two minutes.
Add beef stock, rosemary, and thyme. Nestle ribs and any accumulated juices in the Dutch oven and submerge. Season all over with salt and pepper.
Cover and place in the oven for 2 1/2 hours. Ribs should be fall-off-the-bone tender. Remove from the oven and let rest for 15-20 minutes covered before serving. Skim the fat off the top with a spoon. Shred ribs and remove bones and any chunks of fat.
For the panko topping, heat butter and oil in a pan over medium heat. Add panko and toss until golden.
To serve, add a splash of reserved pasta water to shortribs/sauce to thin. Stir in gnocchi and serve topped with toasted panko and parsley.