Preheat the oven to 350ºF.
Prepare the steak by cutting off the excess fat and then dicing it into 1-inch cubes. Reserve the fat.
Sauté the excess fat in a large ovenproof saucepan over medium heat. Remove and discard the fat, leaving only the grease.
Dredge the steak cubes in 1/4 cup flour, shaking off any excess, then brown them in the saucepan with the fat drippings. Remove the steak and set aside.
In the same saucepan, combine the onions, carrots, mushrooms, celery and garlic. Sauté over medium-low heat until the vegetables begin to soften.
Stir in the herbs and tomato paste, cooking until the tomato paste begins to caramelize, about 1 minute, then stir in 1 Tablespoon of flour.
Deglaze the saucepan by adding the wine and beef broth and stirring, scraping up any brown bits, until a smooth sauce forms. Taste and season the sauce with salt and pepper.
Cover the saucepan, transfer it to the oven and allow it to cook for 20 minutes.
Remove the saucepan from the oven, add the reserved steak (with any juices) and then return it to the oven for an additional 15 minutes.
Serve the beef over buttered parsley noodles (recipe below).