Peel the potatoes and cut into thin slices. Put in a saucepan, add milk, cream, squeezed garlic, salt and lemon pepper and bring to the boil. Cook over low heat for about 10 minutes, stirring frequently.
Preheat the oven to 200 degrees circulating air.
While the potatoes are simmering, peel the asparagus in the lower third and cut off the woody ends. Cut the asparagus tips about 5 cm long, put them to one side and cut the remaining stalks into 1 cm thick slices. Finely chop the dill.
Add the asparagus slices to the potatoes, bring to the boil briefly, then mix in the dill and distribute everything in a buttered casserole dish. Spread the asparagus tips on top, sprinkle with grated Parmesan and bake in the preheated oven for about 15 minutes.