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Several brisket recipes here for a smoker.
Smoked Whole Brisket With Burnt Ends
The Beefiest, Juiciest Brisket What Am! the Smokyokie Method
I don't have an egg, but have cooked on one and really like them. Just set up your egg for indirect cooking (ceramic stone, pizza stone, or heavy sheet pan) and rub the brisket with a good rub (sugar in a rub is fine under 300F). It probably doesn't matter whether the fat side is up or down.
Establish a heat level of 250 to 300F and use smoking chips for flavored smoke. I like a large handfull of wood chips in heavy duty foil with one hole in the pouch. I might add another pouch after 2 - 3 hours of smoking.
Smoke for about an hour a lb (.8 hrs/lb for a flat) until interior temperature is 190 to 200F.
Alternatively, when the meat is 160 to 170F, wrap double in heavy duty foil and cook until internal temp is 190 to 200F. This speeds up the process and gives a juice that is excellent when defatted and used to pour over the sliced product.
Red