It used to be that home cooks used every edible part of an animal. Today, we call that "nose to tail" but back in the day, it was common sense. Farmers would butcher animals, usually in the fall when the weather turned cooler, and then it was a race to either eat or preserve all that they could.
Livers, tongues, kidneys, lungs, and brains were all on the menu. And especially in the South, brains, and eggs became a breakfast staple both for everyday meals and special occasions. In a 1992 piece in The Washington Post, Edna Lewis (who helped bring regional Southern cooking into the mainstream) talks about their family Christmas breakfast of "crispy fried oysters, scrambled eggs and brains from the fresh-butchered hogs, liver pudding, sausage, and fresh crisp bacon."
There no etymology of brains and eggs as a dish here in the United States, but rural cooks using every part of an animal may have combined the two because of their similar creamy textures. Garden & Gun talked to chef and North Carolina native Vivian Howard, who noted, "When I talk with people about brains and eggs, it's always older people, and they talk about it like it's a cheeseburger like I should know about it."
Although fresh brains may have the norm in rural areas, and it's likely that home cooks preserved brains from their own livestock, American companies eventually started offering canned brains. When meat was scarce during the World War II, residents in more urban areas were encouraged to eat more offal (animal organs), although that campaign wasn't that successful given that many people have an aversion to eating the less-traditional parts of the animal.
Rose Pork Brains with Milk Gravy
Cow brains took a hit in popularity when Creutzfeldt-Jakob disease (also known as Mad Cow disease) entered public awareness in the 1990s, but pig brains are still a thing in some places in the South. Some chefs are finding ways to put it back on restaurant menus and some home cooks turn to a canned version to get their fix.
One company still sells canned pork brains. Rose Brand Pork Brains with Milk Gravy come in 5-ounce cans. We should note that canned brains aren't exactly "healthy," at least if you're counting sodium and cholesterol. The 5 ounce can counts as one serving and has 500 milligrams of sodium (21 percent of what you should have in a day) and 3190 milligrams of cholesterol (1060 percent of the recommended daily value, so maybe go easy on these).