Heat a large cast iron or non-stick pan over medium heat. Cook the bacon strips until crispy, flipping halfway through to cook both sides evenly, about 10 minutes. Transfer the cooked bacon to a plate lined with paper towels to drain. Remove the pan from the heat temporarily so the remaining bacon fat doesn't burn, if necessary.
For the Scrambled Eggs:
While the bacon is cooking, make the scrambled eggs. Whisk the eggs, hot sauce, and a pinch of salt and pepper together in a medium bowl. Heat a new cast iron skillet or non-stick pan over medium heat, and add the olive oil. Add the eggs to the pan and slightly lower the heat, then cook the eggs until scrambled (about 3-4 minutes.)
For the Mashed Avocado:
While the eggs are cooking, make the mashed avocado. Spoon ripe avocado into a bowl and add garlic powder, a pinch of salt and pepper, and fresh lime juice. Mash the avocado until smooth, and set aside.
For the Grilled Cheese:
Combine the shredded cheddar and mozzarella. Set aside.
Return the pan with the bacon fat back to the heat. Divide the softened butter between all four slices of bread, spreading about 1/2 tbsp. of butter onto one side of each slice.
Place one slice of bread, butter side down, into the pan with the bacon fat. Sprinkle 1/3 cup of shredded cheese over the bread, then top the cheese with three slices of bacon. Spoon half of the scrambled eggs over the bacon.
Spread half of the mashed avocado over the scrambled eggs, then top the avocado with 1/3 cup of shredded cheese. Top the sandwich with another slice of bread, butter side up. Use a spatula to gently press down on the sandwich.
Cook the grilled cheese about 2-3 minutes until the bottom side is browned and crispy, then carefully flip. Cook the other side another 2-3 minutes until browned and crispy, then remove from the heat.
Repeat to make the second sandwich. Slice both sandwiches in half, and serve hot!