Heat 2tsp oil in a large nonstick pan over medium-high heat. Add the onions, half the tomatoes, and the thyme; cook until the onion softens, about 5 minutes.
Add the collard greens and season with salt and pepper; continue to cook stirring occasionally, until the collards are tender, about 10 minutes.
In the meantime, combine the remaining tomatoes with the avocado, hot sauce and 1tbsp olive oil in a small bowl; season with salt and toss gently. Set aside.
Heat the remaining oil in a separate skillet over medium high heat. Crack the eggs into the skillet and cook until the whites are almost set, about 3 minutes. Cover and cook till the whites are set but the yolks are still slightly runny, about 2 more minutes; season with salt and pepper.
Meanwhile, toast the rolls. Top each half with 2 slices cheese, some collards and a fried egg. Serve with the avocado salad.