Tie each veal shank with kitchen twine to keep the meat compact. Generously season with salt and let sit for 15 minutes (or refrigerate for a few hours).
Preheat oven to 500°F (260°C). Place shanks on a wire rack over a foil-lined tray, drizzle with olive oil, and roast for 30 minutes until browned.
Roughly chop onion, carrot, fennel, and garlic. Mince these in a food processor until finely chopped but not a paste.
Heat olive oil in a Dutch oven over medium-high heat. Add the minced vegetables and a pinch of salt. Sweat for 10-15 minutes until softened.
Add anchovies and tomato paste into the veggies, stirring and cooking for 2 minutes. Add butter and melt. Add a splash of water here if the bottom of the pot is starting to get brown.
Stir in flour to form a weak roux. Cook for about 30 seconds.
Add red wine, scraping the bottom to deglaze. Cook for 2-3 minutes.
Add Better Than Bouillon and beef stock. Bring to a simmer then nestle the seared shanks into the liquid along with any veal cooking liquid from the roasting pan (if it's not burnt). Cover and braise in a 300°F (150°C) oven for 2 hours, checking at 90 minutes. Cook uncovered for the last 30-40 minutes.
Cool braise at room temp for 2 hours then refrigerate overnight for best flavor.
To finish, reheat over medium-low heat, scraping the pot bottom. Reduce liquid by 30-40%.