Heat 2 teaspoons olive oil in a large nonstick skillet over medium-high heat. Add the Canadian bacon and cook, stirring occasionally, until it starts browning, about 2 minutes. Add the onion, half of the tomatoes, and the thyme; cook until the onion softens, about 5 minutes. Add the collards and season with 1/4 teaspoon salt and a few grinds of pepper; continue to cook, stirring occasionally, until the collards are tender, about 10 minutes.
Meanwhile, combine the remaining tomatoes, the avocado, hot sauce and 1 tablespoon olive oil in a medium bowl; season with salt and gently toss. Set aside.
Heat the remaining 1 teaspoon olive oil in a separate large nonstick 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 until 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.