Preheat oven to 350°F. Grease a 13x9-inch baking dish with butter or non-stick cooking spray.
In a large skillet, melt 1/4 cup of the butter over medium heat. Once melted, whisk in flour. Cook for about 1-2 minutes, until bubbly but not browned.
Gradually whisk in evaporated milk or half and half, milk, garlic powder, and salt and black pepper. Cook, stirring constantly, until the mixture thickens and is smooth, about 3-5 minutes.
Remove from the heat and stir in American or Velveeta cheese and 4 ounces of the cheddar cheese until melted and smooth.
Pour the frozen broccoli florets in the skillet, and stir until the broccoli is evenly coated.
Transfer the mixture to the prepared baking dish, spreading it in a single layer.
Melt the remaining butter in a medium bowl in the microwave. Combine the melted butter with the remaining cheddar cheese and cracker crumbs. Sprinkle the cracker mixture evenly over the top of the casserole.
Bake uncovered 30-35 minutes, or until bubbly and the top is golden brown.