Adjust oven rack to lower position and preheat oven to 275°F. Season bison with salt and pepper. Heat oil in a large Dutch oven over high heat until lightly smoking. Place bison in Dutch oven and cook without moving until first side is deeply browned, about 8 minutes. Turn and cook until second side is browned, about 6 minutes longer. Continue turning and cooking until all sides are browned, about 8 minutes longer (22 minutes total), reducing heat if oil is smoking excessively. Transfer to a large platter.
Add onions, celery, and carrots to pot and cook, scraping up any browned bits from bottom. Reduce heat to medium and continue to cook, stirring occasionally, until onions are deeply browned, about 16 minutes total. Stir in anchovies, half of rosemary, tomato paste, and soy sauce, and stir until homogenous.
Whisk in beer and stock. Return chuck roll to pot and add bay leaves and rosemary stems. Bring to a boil, cover, and transfer to oven. Cook until a skewer or knife inserted into the bison meets little resistance, about 4 hours.
Remove from oven and allow to cool for two hours, and then transfer to refrigerator overnight. The next day, remove bison, untie string, and slice. Reheat sauce until simmering, season to taste with salt and pepper, then add bison slices and carefully heat through. Sprinkle with remaining rosemary and serve immediately.