This plant, apparently a giant fennel, provided several of the most important sauces and condiments of ancient Greece and Rome, as well as medicinals there and in Egypt. Juice from the stems and roots, the stems themselves and most important the resin exuded from cuts just above the root were used. So important was this plant to the ancient cuisines they cannot be accurately reproduced without it. Unfortunately it is not currently available due to presumed extinction (some still hope it can be found somewhere in the wilds of Libya).
While other members of the fennel family have been sold as "silphium", true silphium grew only around the city of Cyrene in Libya, North Africa. While Pliny wrote that silphium of Cyrene was extinct in the 1st century CE, it appears from other writers it still existed there in the 5th century CE, but they may have mistaken another fennel for it. Several varieties of African fennel have been proposed as "silphium" but all ancient representations of the plant distinctly show a striated stem and leaf petioles in nearly opposite pairs. No fennel like this has yet been found. Ferula tingitana is thought to be the nearest living relative. Photo of coin from Cyrene believed in the public domain.
More on Fennels.
Greek and Roman writers did not describe silphium's taste characteristics in detail - everyone already knew them. What we do know is that Asafoetida, available with somewhat different characteristics from various regions, was considered inferior to true silphium. In particular silphium did not have the sulphurous odor asafoetida has. This is, however, a point of similarity we can work from. Since asafoetida is as close as we can get today, it is good that the unmistakable smell of SAE 90 weight hypoid gear oil disappears if the resin is properly fried in hot oil for just a few seconds before adding other ingredients.
Other parts of the plant were also used but are now unavailable except in Persia and Afghanistan where asafoetida is grown. I have developed a recipe, Laser Root / Stem / Juice to fake up a substitute.