Combine avocado and beans in a bowl. Mash with a fork until avocado is smooth and beans are half-mashed. The beans can be more difficult to smash, so take your fork and press them against the sides of the bowl.
Add in the shredded cheddar (optional), sea salt and pepper. And whatever other seasonings you prefer! Cumin? Hot sauce? Go for it!
Spread avocado mixture over toast. Top with your egg.
Recipe by Modern Martha at http://modernmartha.com/2014/01/avocado-white-bean-egg-toast/