In a pot of boiling water, blanch broccoli for 3 minutes. Drain well and set aside.
In a large skillet over medium-high heat, add 1 tbsp. butter and oil.
When it starts sizzling, working in batches, add chicken cubes; season with salt and pepper. Sauté until light golden, about 4 to 5 minutes.
Transfer to a bowl while cooking the remaining cubes.
Reduce the heat to medium and add onions; season with salt. Sauté for 2 minutes, scraping the bottom of the skillet to dislodge any brown bits.
Add mushrooms, 1 tbsp. butter and season with black pepper. Stir until butter is melted before adding the remaining 2 tbsp. butter. Cook for 5 minutes, stirring often.
Add garlic and sauté for 1 minute.
Sprinkle in flour, stir until the ingredients are coated and cook for 2 minutes.
Slowly pour in chicken broth and scrape the bottom to release any stuck ingredients. Add heavy cream and stir to blend.
Add Dijon mustard and bring to a simmer. Cook until the sauce thickens and coats the back of the spoon.
Preheat oven to 375ºF and grease 3-quart baking dish and set aside.
Add sour cream, cooking sherry and lemon zest; stir to blend.
Add cheese and stir until melted. Stir in hot paprika.
Add cooked chicken cubes including any accumulated juices and broccoli florets; mix until blended.
Remove from the heat and transfer the mixture to the prepared baking dish; set aside.
In a small bowl, combine panko, cheese and melted butter; stir to combine. Evenly sprinkle topping over the chicken mixture.
Transfer to the preheated oven and bake until the top is golden brown, about 23 to 25 minutes.
Remove from the heat and let it rest for 10 minutes before sprinkling on some chopped parsley. Serve over egg noodles or rice.