Prepare artichokes or buy canned bottoms. To prepare remove stem and then break the leaves of the base. Artichoke should have a conical shape when done. Cut off the core of the artichoke above the base. Base should be trimmed with vegetable peeler until all of the fibrous material is removed. Place the core and bottom in lemon water. The choke will be removed after cooking.
Arrange artichoke pieces in one layer in saucepan with little oil, water, lemon juice and a dash of salt. Cook for 20-25 minutes covered. Once tender remove bottoms with spoon and pour cooking liquid over the bottoms.
Cook in skillet with dash of salt 3-4 minutes until wilted. Drain. Using a spoon, press spinach to extract water. Chop the spinach and sprinkle with salt and pepper. Heat butter in skillet until dark brown then add spinach. Sauté just until heated. Reheat the artichoke bottoms in their liquid and drain. Arrange them in a gratin dish and spoon spinach into each one. Press the Swiss cheese on top of spinach.
Melt the butter in a heavy saucepan and add flour. Mix with whisk and cook on medium heat for 10 seconds. Add the milk all at once and mix with whisk. Add the salt, pepper, and nutmeg. Stir until sauce boils. Reduce heat and boil for 30 seconds. Add cream and remove from heat.
Preheat the broiler. Coat the artichokes with sauce and sprinkle with parmesan cheese. Heat under broiler for 3-4 minutes or until browned.