Ingredient Notes: To clean leeks: Trim roots and ragged tops. Slice leeks and place in plenty of water, then drain. Repeat a few times. The slices do not absorb water or lose flavor. The "cooking sherry" sold in many supermarkets can be surprisingly high in sodium. We prefer dry sherry, sold with other fortified wines in your wine or liquor store.
Preheat oven to 375 degrees F. Coat a 7-by-11-inch (2 quart) glass baking dish with cooking spray.
Place chicken in a medium skillet or saucepan and add lightly salted water to cover. Bring to a simmer over high heat. Cover, reduce heat to low and simmer gently until the chicken is cooked through and no longer pink in the center, 10 to 12 minutes. Drain and slice into bite-size pieces.
Heat oil in a large nonstick skillet over medium-high heat. Add leek and salt and cook, stirring often, until softened but not browned, 3 to 4 minutes. Add flour; stir to coat. Add broth, milk, sherry, thyme and pepper and bring to a simmer, stirring constantly. Add broccoli; return to a simmer. Remove from heat and stir in 1 /2 cup Parmesan, mayonnaise and mustard.
Spread half the broccoli mixture in the prepared baking dish. Top with the chicken, then the remaining broccoli mixture. Sprinkle evenly with the remaining 1 /2 cup Parmesan. Bake until bubbling, 20 to 25 minutes. Let cool for 10 minutes before serving