Heat the oil in a large heavy bottomed pot or dutch oven until hot but not smoking. Toss the veal with salt, pepper, and 2 Tbsp flour and add to the pan.
Stir in the flour, scraping up the brown bits on the bottom of the pan. Add the anchovy paste, soy sauce, and sugar. Whisk in the wine, then the milk, and finally the chicken stock.
Bring to a boil and reduce to a simmer. Add the thyme sprigs, browned veal, potatoes and mushrooms to the pot. Season well with kosher salt and pepper.
Cover and simmer gently over very low heat for at least 2 hours, or until the veal is tender. Remove the sprigs of thyme. Season to taste and serve over cooked pasta or rice.