Place eggs in a saucepan, cover with water, bring to a boil, then remove from heat and let sit for 10 minutes.
Transfer eggs to an ice bath, peel, and dice into 1/2-inch pieces.
Halve the avocado, remove the pit, and scoop the flesh into a medium mixing bowl.
Mash the avocado with a fork until mostly smooth but slightly chunky.
Add the diced eggs, mayonnaise, lemon juice, salt, and pepper to the bowl and fold gently to combine.
Toast the bread slices until golden brown and firm.
Divide the avocado egg salad evenly between the two slices of toast.
Dust the tops with smoked paprika and garnish with chopped chives before serving.