Season the Chicken: Pat the chicken breasts dry with paper towels. If they are very thick, gently pound them to an even thickness. Season both sides with garlic powder, paprika, salt, and black pepper.
Cook the Chicken: Heat the olive oil in a skillet over medium heat. Add the seasoned chicken and cook until golden on both sides and fully cooked through. The internal temperature should reach 165°F. Transfer the chicken to a cutting board and let it rest for about 5 minutes.
Prepare the Avocado: Cut the avocados in half and remove the pits. Scoop the flesh into a bowl and gently mash with lemon juice, salt, and black pepper. Leave a few small pieces of avocado intact for a pleasant texture.
Prepare the Bread: Spread mayonnaise evenly over one side of each slice of bread. Keep the layer relatively thin so the sandwich doesn't become too heavy.
Build the Sandwich: Slice the rested chicken into thin pieces. Place the chicken on four slices of bread, then add the mashed avocado and a slice of cheddar cheese. Top with the remaining bread slices.
Toast the Sandwich: Melt the butter in a clean skillet over medium-low heat. Carefully place the sandwiches into the skillet and cook until the bottom is golden brown and crisp.
Flip and Melt: Carefully flip each sandwich using a spatula. Continue cooking until the second side is golden and the cheese has completely melted. Reduce the heat if the bread begins browning too quickly.
Slice and Serve: Transfer the sandwiches to a cutting board and let them rest for 1–2 minutes. Slice each sandwich diagonally and garnish with fresh parsley if desired. Serve warm.