What can I use in place of eggs for brownies?

If you have a can of chickpeas, you can use the liquid from that. It takes about 3 tablespoons of aquafaba to replace each egg. You can also use mayonnaise, in the same 3 tablespoons per egg replacement ratio. That actually works nicely because it will replace some of the fat lost by not using an egg yolk. Your brownies will likely end up more on the fudgy side than cakey, and you also want to cut back on the oil a little, maybe by a couple tablespoons.