Lightly grease a 9-inch square baking dish.

Place the diced potatoes in a pot of salted water. Bring to a boil and cook until just tender, but slightly undercooked since they will continue to cook in the oven. Drain the potatoes well and transfer them to the prepared baking dish.

Heat a large nonstick skillet over medium-high heat. Add the oil and sausage, cooking until the sausage is browned. Remove the sausage from the skillet and add it to the baking dish with the potatoes.

Wipe the skillet clean and melt the butter over medium heat. Add the flour and cook, stirring constantly, for 1 minute.

Gradually whisk in the half-and-half, bringing it to a simmer. Add the garlic powder and stir. Lower the heat and add the Velveeta cheese, stirring until fully melted.

Stir in half of the shredded cheddar cheese until melted. Remove from heat and taste for seasoning, adjusting with salt and pepper as needed.

Pour the cheese sauce over the potatoes and sausage in the baking dish. Sprinkle the remaining cheddar cheese on top.

Bake in a preheated 350°F oven for 25 to 30 minutes.