Baking without egg does not necessarily require baking from scratch.
These are my favorite two ways to make eggless brownies from a boxed brownie mix.
(1) Take a can of black beans. Drain and rinse the beans. Return the beans to the can and fill the can to the top with water. Puree the beans and water in a food processor until very smooth. Add the bean puree to the brownie mix and stir to combine well. Bake according to package directions. You may need to add just a couple of minutes if your oven is fussy like mine. This version is dense enough to stand up to some mix-ins like chocolate chips, orange zest, chopped cystallized ginger or nuts.
(2) Instead of bean puree use 1 Cup of sour cream and an extra teaspoon of baking powder. This makes a slightly more delicate brownie that doesn't stand up quite as well to mix-ins, but my spouse prefers the texture and flavor over the bean version. Maybe I am just a hog for chocolate, but I like them equally well.