https://www.theatlantic.com/technology/archive/2013/10/why-do-witches-ride-brooms-nsfw/281037/

"In the Europe of the Middle Ages and into the Renaissance, bread was made, in large part, with rye. And rye and rye-like plants can host fungus—ergot*—that can, when consumed in high doses, be lethal. In smaller doses, however, ergot can be a powerful hallucinogen. Records from the 14th to the 17th century mention Europeans' affliction with "dancing mania," which found groups of people dancing through streets—often speaking nonsense and foaming at the mouth as they did so—until they collapsed from exhaustion. Those who experienced the "mania" would later describe the wild visions that accompanied it. (In the 20th century, Albert Hofmann would realize the psychedelic effects of LSD while studying ergot.)

So why do the brooms fit into this? Because to achieve their hallucinations, these early drug users needed a distribution method that was a little more complicated than simple ingestion. When consumed, those old-school hallucinogens could cause assorted unpleasantnesses—including nausea, vomiting, and skin irritation. What people realized, though, was that absorbing them through the skin could lead to hallucinations that arrived without the unsavory side effects. And the most receptive areas of the body for that absorption were the sweat glands of the armpits ... and the mucus membranes of the genitals.

So people used their developing pharmacological knowledge to produce drug-laden balms—or, yep, "witch's brews." And to distribute those salves with maximum effectiveness, these crafty hallucinators borrowed a technology from the home: a broom. Specifically, the handle of the broom. And then ... you get the idea."