Lay out the croissant halves. On the bottom halves, place 3/4 cup of the leftover chicken salad. Top with a handful of arugula and layer with slices of avocado, tomato and Cheddar. Season with salt and pepper, and top with the croissant tops.
Heat a grill pan and a heavy skillet over medium heat. Transfer the sandwiches to the grill pan and set the skillet directly on top, to weight. Grill until the sandwiches are golden and the cheese is melted, 4 to 5 minutes.
Billie's Houdini Chicken Salad:
In a large stockpot over high heat, cover the chicken with water and bring to a boil. Cook for 20 to 30 minutes, or until tender. Drain and set aside to cool completely, about 20 minutes, then dice.
In a large bowl, mix together the chicken, yogurt, grapes, almonds, pecans, cranberries, apples and onions. Season with salt and pepper to taste. Serve on toasted bread or with crackers.