Pour the flour, eggs, and salt in a mixer fitted with a dough hook, and mix until the mixture forms a dough. Knead the dough for 5 minutes in the mixer. The dough should form a ball and be climbing up the dough hook. Add in 1 tablespoon of extra-virgin olive oil and 1/2 a ladle of lukewarm water and mix until well combined. Remove the dough from the mixer, cover with plastic wrap and let sit at room temperature for 20 minutes. Roll out with a pasta machine.
Squeeze the lemons into a bowl of cold water. Peel and clean the artichokes and plunge them in water and lemon so they don't brown. One by one, slice the artichokes very thinly (you can do this on a mandoline if you prefer), returning to the ice water as you finish. Julienne the strips and return to the acidulated water.
Brown the garlic in extra-virgin olive oil. Drain the artichokes and add them with a pinch of salt and pepper. Cook on high heat for 8 minutes, then pour in the fresh cream and reduce it all for about 10 minutes. Perfume with fresh marjoram.
Wash the tomatoes and plunge them into boiling water for 10 seconds, then plunge them in ice water. Peel them, seed them, and dice them. (Set aside a few tablespoons of diced tomato for garnish.) Get 2 sheets of egg pasta, boil them in salt water, let them cool and cut them with the help of a circular pasta cutter until you have 24 little disks. In an oiled cake pan arrange 4 individual pasta disks and put the artichokes, grated Parmigiano-Reggiano, and tomatoes on top. Repeat the procedure 5 times, making 6 layers.
Preheat the oven to 360 degrees F (180 degrees C). Bake for 8 minutes. Arrange portions of the lasagna in the center of 4 plates and garnish with diced tomatoes, marjoram leaves and drizzle everything with extra-virgin olive oil. Serve hot.