Preheat the oven: preheat the oven to 180°C / 350-375°F / Gas Mark 4-5.
Potatoes: use a vegetable peeler and cutting board to peel the potatoes and then discard the skins. Next use a mandolin to thinly slice the potatoes.
Cream sauce: add the cream, garlic powder, dried thyme, salt and pepper to a medium sized jug and use a spoon to whisk until consistently combined.
Combine: add the sliced potatoes, diced onion and broccoli florets to a large mixing bowl. Then use a wooden spoon to stir and combine.
Sauce: next pour the cream sauce over the potatoes, onion and broccoli and again use the wooden spoon to stir and combine.
Baking dish: grease a large baking dish with cooking oil. Then transfer the combined cream and potato mixture into the baking dish. Push any broccoli florets under the potatoes and make the top a reasonably flat surface.
Oven bake: place the potato and broccoli bake into the oven on the middle shelf. Let it bake (uncovered) for 50 minutes. Whilst the cooking time is up, use oven mitts to remove the baking dish and place it onto a heatproof surface. Then use a skewer inserted directly down into the thickest part of the potatoes. It there is any resistance pop it back into the oven for a little bit longer. If the skewer goes straight down with no resistance then top with the mozzarella, followed by the colby cheese. Return the potato bake (with cheese topping) to the oven for a further 10 minutes. Let the cheese melt and turn holden brown in parts.
To serve: once the cheese has melted, use the oven mitts to remove the potato bake from the oven and place it onto a heatproof surface. Let it sit (it thickens during this time) for about 5 minutes. Once there are no visible bubbles sprinkle some chopped parsley over the top and then place it onto the table with a large spoon for serving.