Preheat oven to 350°F.
Pat beef brisket cubes dry and season with salt and black pepper.
Heat olive oil in a large dutch oven over medium-high heat.
Brown the beef brisket cubes in 2 to 4 batches, turning to brown all sides, 5-6 minutes per batch. Avoid overcrowding.
Remove browned beef and set aside on a plate.
Add onions, carrots, and garlic to the pot; cook and brown for 3-4 minutes until softened and fragrant.
Stir in tomato paste and cook for 1 minute.
Return browned beef and juices to the pot; sprinkle with flour and toss to coat evenly. Cook until no dry flour remains.
Pour in red wine; cook for 1-2 minutes while stirring and scraping the browned bits from the pot bottom.
Add beef stock, bay leaf, thyme sprigs, and 2 tablespoons chopped parsley; stir to combine and remove flour lumps.
Bring stew to a boil, cover, and transfer the pot to the oven. Slow cook for 2 hours.
Remove pot from oven, uncover, add cubed potatoes and 1 cup water; stir well.
Cover again and cook in oven for 1 to 1½ hours, or until potatoes are fork tender.
Skim off excess fat from stew surface before serving; remove bay leaf and thyme sprigs.
Garnish with remaining tablespoon of chopped parsley and serve warm.