Eggs do a lot for enriched doughs. They add moisture, they add fats, and they act as an emulsifier. Without eggs, many breads would not exist.
Still, they are a bit of a bother. How do measure 1/2 egg? Easy answer - double your recipe and use a whole egg. But that's always a good answer.
In the case of 1/2 egg, if you are measuring by volume you can beat the egg and use 1/2 of the liquid. If you are measuring by weight, you can beat the egg, weigh the beaten egg and use 1/2 of it. In either case, the question remains as to what to do with the rest of the egg.
Large eggs in the United States average 50 grams each. (No, they didn't train the chickens to lay 50 gram eggs. They sort the eggs. Bigger ones are sold as extra large, smaller ones are medium or small eggs.)
And now, for the sad confession. When it comes to measuring eggs, I cheat. I divide the amount of egg I need by 50 and round the number of eggs. I never round to less than 1. Here, let me demonstrate. Imagine a recipe calls for 35 grams of eggs and 360 grams of water. The total there is 395 grams.
I put a bowl on my scales, zero the scales, add an egg, and then add water to get to the desired combined weight, in this case 395 grams. Easy Peasy.
What do you do if you're a vegan?
Or baking for one? If the eggs are a major part of the bread's flavor profile (such as Challah or Kaiser Rolls), you should probably just pick another recipe, one that is egg free. If the eggs aren't a major part of the flavor profile, like the Carrot Pineapple Cup cakes, you can substitute cooking oil and soy flour for the eggs. For each egg, use about 2 TBSP (10.5 Grams) of soy flour and 3 TBSP (40 Grams) of light olive oil. This should provide a good replacement for the oil and emulsifier the egg provided.