Preheat Oven:
Heat oven to 350°F (175°C).Season Brisket:
Dry brisket cubes thoroughly using paper towels. Season with salt and pepper, mixing well to coat uniformly.Sear Brisket:
In a large (5-6 quart) heavy Dutch oven or stock pot over medium-high heat, warm olive oil. When hot, sear brisket cubes in 2-3 batches, flipping with tongs, for roughly 5-6 minutes each batch. Avoid overcrowding the pot.Reserve Brisket:
Move seared brisket to a plate and reserve.Sauté Vegetables:
Put onions, carrots, and garlic into the pot. Sauté and brown for 3-4 minutes until vegetables begin to soften and garlic becomes aromatic.Cook Tomato Paste:
Mix in tomato paste, stir thoroughly, and cook for 1 minute.Return Brisket:
Return seared brisket and any accumulated juices to the pot. Dust with flour and toss to coat meat and vegetables. Cook until no raw flour remains visible.Deglaze with Wine:
Pour in red wine, stirring and scraping up browned residues from the pot's bottom and sides (deglaze). Cook for 1-2 minutes.Add Stock and Herbs:
Add beef stock, bay leaf, thyme sprigs, and 2 tablespoons parsley. Stir well to combine, breaking up any flour clumps.Braise for 2 Hours:
Bring to a boil, cover pot with lid, and place in the preheated oven. Cook for 2 hours.Add Potatoes:
After 2 hours, take pot out of oven, carefully remove lid. Add potato cubes and 1 cup water, stirring to mix evenly.Finish Braising:
Replace lid and continue cooking in the oven for another 1 to 1 1/2 hours until potatoes are fork-tender.Skim Fat:
Just before serving, use a large metal spoon to skim off excess fat from the surface. Discard bay leaf and thyme sprigs.Garnish and Serve:
Sprinkle with the remaining 1 tablespoon parsley and serve hot.