Quiche, in one or more flavors

Frittata or muffin sized crustless quiches.

Quiche is often better the next day. Let the flavours mingle.

Deviled eggs are also a hit at a party and you can cook the eggs a few days ahead and assemble the day before/ morning of.

There's also strata's (sweet & savory) and the infamous breakfast casserole which is delicious both make-ahead and perfect for a brunch.

I suspect the OP means a break-the-fast for the close of Yom Kippur, rather than a brunch per se. That makes it little difficult to do day-ahead dishes when the focus is getting for an all-day fast that commences in the evening; my take was that Lara meant make prepared-well-in-advance, freezable dishes so that there is little work the day before and none the day of, am I right?

A couple ideas, subject to whether you and your guests like these sort of things:
* Poached eggs can be made in advance (restaurants do it all the time), held up to 2 days, then heated just before serving. Consider something on toast, or in a sauce (like Shakshuka). Technique is here:
http://www.seriouseats...
Some sort of grain-based casserole. We don't think of them, necessarily, as egg dishes, but they are.
* Savory bread pudding
* Savory or sweet noodle kugel