Caramelize the onions: In a large wide pot or deep skillet heat the butter and olive oil over medium heat until the butter begins to bubble softly. Add the onions, reduce heat to low and cook for about 40 minutes, until the onions acquire a deep amber hue.
While the onions are cooking, clean and blanch the artichokes: Squeeze one lemon into a bowl with 3 cups of water. Trim the artichokes: cut away their tough outer leaves, leaving a little of the stem intact. Trim its tough exterior with a paring knife. Using a teaspoon scrape out the purple, fuzzy choke. Rub the artichokes with lemon and place in the acidulated water. Bring a large pot of salted water to a rolling boil. Drain the artichokes from the acidulated water and blanch for one minute. Remove and drop immediately into a large bowl filled with ice.
In a large skillet heat 1 tablespoon olive oil and sauté the potato slices for a few minutes, just until softened. Turn once.
Make the béchamel: In a medium pot over medium heat, melt the butter until it bubbles. When it stops bubbling, add the flour and whisk for about 5 minutes, untiul the flour is golden. Pour in the milk and cream, whisking until thick, about 10 to 12 minutes. Remove from heat and add the eggs, whisking vigorously. Mix in the cheeses. Season with salt and pepper. Set aside.
Toss the herbs together in a small bowl. Preheat the oven to 350°F/170°C. Oil a large baking pan.
To assemble the moussaka: Oil a large roasting pan. Sprinkle a handful of breadcrumbs over the bottom surface. Layer half the potatoes in one layer. Salt and pepper. Sprinkle with a handful of breadcrumbs. Add about a third of the onions and herb mixture. Layer half the artichokes evenly over the surface. Season with salt and pepper and sprinkle with another handful of breadcrumbs. Sprinkle with half the feta, one-third more of the herbs and a third more of the onions. Repeat the layering process in the same order.
Pour béchamel over the surface. Bake uncovered until lightly golden (approximately 55 minutes to 1 hour). Remove, cool slightly, cut into squares, and serve.
