Peel the potatoes and cut them in half. Rinse them under running water and put in a pan.
Fill the pan with enough water so that the potatoes are about 1 cm beneath water level.
Add 1 teaspoon salt to the water.
Bring the water to a boil and cook the potatoes for 20 minutes or until tender. You can check this by pricking the potatoes with a fork. If the fork slides in easy, the potatoes are done. Otherwise, extend the cooking time by 3 minutes and try again.
Peel the asparagus with a peeler. See the tips on how to do this best. Also cut the hard bottom of the asparagus (about 2 cm from the bottom.)
Slice the asparagus into 3 cm pieces.
Melt 2 tablespoons of butter in a frying pan.
Add the leeks and cook the leeks for 3 minutes.
Pour the cream with the leeks and stir well.
Simmer for 5 minutes, stirring occasionally.
Add the asparagus and tarragon to the frying pan, mix well and simmer for another 5 minutes.
Taste now (not before because some moisture evaporates and you can make the dish to salty) and season the vegetable mixture with salt and pepper to taste.
Divide the leek asparagus mixture over the bottom of the baking dish.
Cut the ham into cubes (if you haven't bought ham cubes) and spread them over the leek asparagus mixture.
Cover the dish with potato slices and sprinkle with cheese and chopped parsley.
Bake the oven dish in the preheated oven for 15 minutes.