We have no idea who painted this beyond it was someone in the Netherlands around 1586.
Queen Elizabeth I of England was a longtime supporter of the Dutch. They were connected religiously, with both countries being Protestant, and also economically: the Dutch had the most lucrative trading markets in northern Europe (they create the world’s first stock exchange in 1602), and they produced large amounts of textiles made from English wool.
Here, the healthy, productive cow represents the Netherlands. Elizabeth feeds it, while a Dutch leader, William of Orange, holds it by the horns. Elizabeth has been painted in virgin white with the face of a young woman, which she would have greatly approved of. In truth, she was about 50 years old at the time.
King Philip II of Spain is attempting to ride it, alluding to Catholic Spain’s repeated aggression against the territory it claimed as its own (via inheritance).
Meanwhile, Francis, Duc of Anjou, can’t seem to figure out which end of the cow he should be addressing, and is getting crapped on for his troubles. Francis courted Elizabeth and supported the Dutch against the Spanish right up until he tried taking over several Dutch cities. He also doesn’t appear to be wearing any pants.