Preheat oven to 375 degrees F and oil an 8x8 inch baking dish.
Bring a pot of water to a boil, reduce heat, add chicken and poach, covered, until chicken is no longer pink in the center, about 10 to 12 minutes. Drain, slice into bite sized pieces and set aside.
Heat olive oil in a large skillet over medium high heat. Add shallots and saute' until softened but not browned, about 3 to 4 minutes.
Add flour, stir to coat, add broth, milk, cooking wine, oregano, and pepper and bring to a simmer, stirring constantly. Add broccoli, return to a simmer, remove from heat, and stir in 1/2 of the Parmesan, the mayonnaise, and mustard.
Spread half of the broccoli mixture in baking dish, top with the chicken and then the remaining broccoli mixture. Sprinkle evenly with the remaining Parmesan and bake, uncovered, until bubbly, about 20 to 25 minutes. Let cool for about 5 minutes and serve.
By Deeli from Richland, WA
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