To make the guasacaca, add the avocado, bell pepper, cilantro leaves, onion, jalapeno, garlic, oil, vinegar, and salt to a high-speed blender and blend until smooth. Taste and add more salt, if needed.
In a large skillet over medium-high heat, add the olive oil. Once the oil is hot and shimmering, add the sausage, breaking it up with the back of a spoon or spatula. Cook until deeply browned and cooked through, breaking it up into smaller chunks, about 5 minutes. Transfer to a bowl lined with a paper towel. Pour out any excess oil, if desired, leaving about 2 teaspoons behind for the eggs.
In the same skillet over medium-high heat, add the eggs and salt and cook, stirring gently to form large curds, until almost cooked through, about 1 minute. Add the sausage back to the pan and stir it all together. Remove from heat, transfer back to the bowl and cover with tinfoil or a cloth to keep warm. Carefully wipe out the skillet.
In the same skillet, over medium-low heat, add the tortillas, sprinkle 2 tablespoons cheese onto each tortilla to cover. Warm until cheese is melted, about 1 minute. Transfer tacos to your plate and top with the sausage-egg mixture, plenty of guasacaca, cilantro stems and red onion, if using.
Store leftover sauce in the fridge for up to 5 days.