Pat beef cubes dry and sprinkle with salt and pepper. Heat oil in a 6- to 8-quart wide heavy pot over moderately high heat until hot but not smoking, then brown meat well on all sides, about 10 minutes total. Transfer with tongs to a platter.
In fat remaining in pot, cook onions over moderate heat with bay leaf, stirring occasionally, until golden, 10 to 12 minutes. Place beef with onions in pot. Add beer, veal demi-glace and balsamic (liquid should come about halfway up sides of meat) and bring to a boil.
Cover pot and reduce heat to a low simmer. After about 2 hours add the baby carrots, peas and mushrooms. Turn the heat up slightly and simmer, uncovered, for 30 minutes more, until the vegetables and meat are tender. Season with salt and pepper. Garnish with chopped parsley and chives.
