Preheat your oven to 375°F (190°C). Lightly grease a 9x13 inch (23x33 cm) or similar 2.5-quart baking dish.
Steam the broccoli florets until crisp-tender, about 3 to 5 minutes. You can do this in the microwave with a splash of water or on the stovetop. Drain well and set aside.
In a large skillet or Dutch oven, melt 4 tablespoons of butter over medium heat. Add the chopped shallot and cook until softened, about 2 minutes. Stir in the minced garlic and cook for another minute until fragrant.
Whisk the flour into the skillet to form a paste and cook for one minute, stirring constantly. Gradually whisk in the stock, followed by the half-and-half. Bring the mixture to a simmer and cook, whisking often, until the sauce thickens, about 5 minutes.
Remove the skillet from the heat. Stir in the Dijon mustard and shredded cheddar cheese until the cheese is fully melted and the sauce is smooth. Season with salt and pepper.
Gently fold the cooked turkey and steamed broccoli into the cheese sauce until everything is evenly coated.
Pour the mixture into your prepared baking dish. In a small bowl, melt the remaining 1 tablespoon of butter. Add the breadcrumbs and Parmesan cheese, and toss to combine. Sprinkle the breadcrumb mixture evenly over the casserole.
Bake for 25 to 30 minutes, or until the filling is hot and bubbly and the topping is golden brown. To ensure it's done, a thermometer inserted into the center should read 165°F (74°C).
Let the casserole rest for 5 to 10 minutes before serving. This helps the sauce set up a little.