Great question — answering as the UphillTech team:
Egg yokes contain molecules called lecithins that act as an emulsifier (something that helps oils to mix with water). I'm guessing the brownie mix calls for canola oil to be added, which is what is causing it to come out oily. You can address this in a couple ways. Substitute the oil with butter. Butter is already an emulsion itself, and so will tend to separate less from the liquid ingredients. This will make the brownies thicker when cooled, so the mouthfeel will be less moist. Substitute 1 Tbsp soy lecithin (available from Amazon) per egg yolk. This is the most direct way to compensate. Egg whites also have useful material properties for baking. They act as a leavening agent and also...
Full answer by eyeExWhy: https://cooking.stackexchange.com/a/84250 (CC BY-SA 3.0).
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