Preheat your oven to 375°F (190°C).

In a large oven-safe skillet, heat the olive oil over medium-high heat. Add the chicken pieces and cook until lightly browned on all sides. You don't need to cook them through at this stage. Remove the chicken from the skillet and set aside.

Add the broccoli florets to the same skillet. If the skillet is dry, add a splash more olive oil or a tablespoon of water. Cook for 3-5 minutes, stirring occasionally, until the broccoli is bright green and slightly tender-crisp. Remove the broccoli and set aside with the chicken.

In the same skillet (no need to wipe it clean), melt the butter over medium heat. Whisk in the flour until smooth, cooking for about 1 minute to remove the raw flour taste. Gradually whisk in the chicken broth and milk until the mixture is smooth and begins to thicken.

Reduce the heat to low and stir in the shredded cheddar cheese until melted and the sauce is smooth. Stir in the mayonnaise, Dijon mustard, salt, pepper, and garlic powder. Cook for another 2-3 minutes, stirring constantly, until the sauce is heated through and creamy. Do not boil.

Return the browned chicken and blanched broccoli to the skillet, gently stirring to coat them evenly in the sauce.

If your skillet is not oven-safe, transfer the mixture to a 9x13 inch baking dish.

Bake for 20-25 minutes, or until the sauce is bubbly and the chicken is cooked through. If using, sprinkle with toasted slivered almonds during the last 5 minutes of baking.

Let stand for 5 minutes before serving.