Lightly grease a 20cm round cake pan or springform tin. Carefully stack the potato slices upright in a circular pattern around the edge of the pan, gradually working inward to fill the centre. Arrange the slices closely together, allowing the natural formation to hold its shape.
In a large jug, combine the thickened cream, milk, finely grated parmigiano cheese and French onion soup mix. Season the mixture with salt, then whisk thoroughly with a fork to incorporate the cheese and soup powder evenly.
Pour the cream mixture over the potatoes, ensuring it fills the gaps and settles throughout the dish. Cover with thyme leaves and move them around the cream mixture so they're half out. Season with cracked black pepper.
Cover the pan tightly with foil. If using an Instant Pot with an air fryer lid, place the pan inside, attach the lid, and select the Bake function. Set the temperature to 180°C and cook for 2 hours.
After 2 hours, carefully remove the foil and return the air fryer lid. Increase the temperature to 200°C and continue baking for a further 30 minutes, or until the top is golden and the potatoes are tender all the way through.
Allow the bake to stand for 10 minutes before serving. Garnish generously with fresh dill sprigs and a final crack of black pepper.