The New York Public Library has a collection of hotel menus dating back to the 19th century and including menus from three Boston hotels, only one of which still stands, at the corner of School and Tremont streets.
But while the 1858 menu from the Parker House includes such delicacies as stewed eels, mock turtle soup, mutton cutlets in soubise sauce and nectarine ice cream, there's nary a Parker House roll to be had.
Exactly when Parker House rolls came into being is a matter of some dispute. The Oxford Encyclopedia of Food and Drink in America claims they came into being in the 1870s, when an angry hotel pastry chef (cause of anger unknown) began flinging mounds of dough into an oven. But here's a recipe for Parker House rolls, famous Parker House rolls, from the Ohio Farmer from 1869 (with bonus free recipe for a wart remover):
By 1873, the rolls had spread to England. By 1879, the War Department was including a recipe in its Manual for Army Cooks.
Today, the hotel still offers the rolls, along with Boston cream pie, also invented there (and also not in the 1858 menu's desert section, which includes olives as a way to end one's meal).
H/t Barry Shein.