If the Christmas dinner is a time for lavish acts of culinary excellence, then Boxing Day — celebrated on December 26 every year — is about taking it easy, and making do with what's left over from the previous day's excesses. "Taking it easy" in the UK means Boxing Day Rolls, or Boxing Day Sausage Rolls if we're being pedantic. These are simply (as their name no doubt indicates) sausage rolls that are made on Boxing Day, but they're a popular finger food/snack with variations around the world for all that.
The British and Irish make their sausage rolls (on Boxing Day or otherwise) with puff pastry, baked to golden, flaky and buttery perfection. Inside is a savoury meat filling — ground pork typically, cooked with spices and onions — shaped into a log, then rolled into a sheet of pastry, and baked with a light egg wash.
When these sausage rolls originated isn't clear, although several accounts trace it to: 1. 17th-century peasants who wanted a hardy meal they could carry to the fields, and eat during a pause in their labours; and 2. A December 26 tradition when the British upper classes would give a post-Christmas holiday to their help; left to fend for themselves, they would bake these sausage rolls for their day's meals. In any case, as these accounts also note, putting meat in dough isn't the exclusive prerogative of any one region or time or cuisine; people all over the world have taken recourse to some version of the dish. (For instance, the Germans, French, Czech and Mexicans have types of sausage rolls in their cuisines.) In fact, some food historians believe that the sausage roll came to the English from Asia, via the Silk Road, except it was fish and not pork that was baked into the original.
From the UK, these sausage rolls travelled to the US, where they took on the name "pigs in a blanket". But it isn't exactly the same dish. In the American version, the outer layer is made of croissant or biscuit dough, while the filling comprises an actual sausage or hot dog. To make matters more confusing, there is already a dish called "pigs in blankets" in the UK as well — except Americans would be hard pressed to recognise how the English and Irish make it: wrapping cocktail sausages/chipolatas in slices of bacon, and then baking or pan-frying the meat. (In the UK, this dish is sometimes referred to as "kilted soldiers".)
Back to sausage rolls: while the UK doesn't have very clear indications of when the dish may have been birthed, in America, the first printed recipe for it is to be found in Betty Crocker’s Cooking for Boys and Girls, dated 1957. A caveat: while this is the first recipe that's closest to how the dish is made by Americans today, there is an older mention of "pigs in a blanket" in The Universal Cookery Book: Practical Recipes for Household Use, published in 1887. No "pigs" are involved in the recipe at all; instead, it calls for large oysters to be wrapped in streaky English bacon and fried.