Preheat the oven to 350°F (175°C).

Slice the brioche buns in half and place them on a baking sheet. Toast in the preheated oven for about 5 minutes, until lightly golden.

In a bowl, mash the avocado with a fork.

Add lime juice, salt, and black pepper to the mashed avocado. Mix well.

In a frying pan, heat olive oil over medium heat.

Crack the eggs into the frying pan and cook until the egg whites are set but the yolks are still runny, or cook to your preference.

Place a generous scoop of the smashed avocado mixture on the toasted brioche bun bottoms.

Top the avocado with the fried eggs.

Place the top half of the brioche bun on top of the eggs to create a sandwich.