Thanks, all.
The evil empire was inspired a bit by the Vogons of Hitchhiker's Guide fame. I wanted them to be big goons with a leaning toward bureaucracy and greed, Capable of physical destruction as much as "administruction" through declarations such as; "People of planet X, we now own this planet. Anyone who fails to pay taxes will be subject to the forceful, permanent, and non-negotiable plugging of three orifices' of our choosing." Of course, depending on the species that could be fatal or slightly inconvenient. The E.E. doesn't really concern themselves with the details.
For the purposes of my gaming world, the typical run-in with the E.E. is slightly less threatening. The galaxy is a big place, and the Empire's core is a long way from Bakwotter. Still, like any entitled civilization, they send out exploratory missions to "claim territory" by edict. So far from the core, these are little more than unenforceable bluffs. There isn't the persistent and crushing might of the full empire way out where the explorers roam, but that doesn't reduce their pomp and threats. It does mean that an exploratory team could wander into the wrong bar, throw down an "all your base belong to us" and manage to get killed in the ensuing brawl.
Learning of the destruction of an exploratory team might bring a great deal of harrumphing, but it is unlikely that the E.E. will care to send a full invasion force across the known galaxy for the sake of punishing a small group of hostile homesteaders. Besides, if the exploratory team had been worthy, they would have certainly subjugated the locals and established a new colony. No great empire is built on the back of losers who get snuffed by some drunken rabble. Thus, the E.E. is far more likely to blame the exploratory team for their clearly undersized genitals, heap scorn on the brood mother who whelped them, and go back to bragging about how "In my day I'd have shown those so-and-so's what for!"
It isn't always clear to the locals whether the vague threats are likely to be enforced, so there are cases where some planets capitulate and others give the E.E. a sound flogging. Most races have had some interaction with the E.E. and the fact that many other empires, large corporate strongholds, and independent planets still exist points to the fact that the E.E. may get most of what they have through bullying more than outright martial might.