In any recipe for bread or baked goods, you can make the following substitutions:
plant based milk for milk
For eggs: one tablespoon flaxseed meal whisked together with 3 tablespoons water = one egg. The mixture has to sit a couple of minutes; it will thicken and get to the consistency of a whisked egg. I just do this before I assemble the rest of the ingredients.
Vegan margarine for butter. For pie crusts, I use vegetable shortening. For brushing on bread dough before rising, I use olive oil.
That's all you need to veganize baked goods (except meringues).