Preheat the oven to 350°F. Line a baking sheet with parchment paper.
In a bowl, add the Parmesan cheese, almond flour, baking powder, garlic powder, sea salt, black pepper, and eggs and mix until smooth. Divide the dough into 2 balls.
On a flat surface, roll each ball of dough into 2 rectangles.
Arrange on the prepared baking sheet and bake for 15 minutes. Remove from the oven and let cool for 5 minutes. Cut into each rectangle in half to make 2 square pieces of bread.
In a large skillet, heat the butter over medium heat. Arrange the bread slices in the skillet and toast the bread for 2 minutes, flipping over after 1 minute.
Spread the avocado oil mayonnaise on 2 bread slices. Add the lettuce leaves, tomatoes, and bacon. Top with the remaining bread slices.