Grate cauliflower on a box grater. Transfer to a large bowl and mix with 1 egg and a large pinch of salt.
In a large skillet over medium heat, heat olive oil. Add 2 big scoops of cauliflower mixture to pan and shape into a round patty. Repeat to make a second patty. Let cook until golden brown, about 5 minutes, then carefully flip. Cook 3 more minutes. Transfer to a plate.
In same skillet, fry remaining 2 eggs and set aside.
In a small bowl, mash avocado with lemon juice. Season with salt. Spread on top of cauliflower “toast.” Sprinkle with red chili flakes. Top each with a fried egg.