Cut the potatoes crosswise into 1/8-inch-thick slices. In a large nonstick skillet heat 1 tablespoon of the oil over medium-high heat. Add one-fourth of the potato slices; cook for 4 to 5 minutes or until potatoes are tender, turning once halfway through cooking time. Transfer potatoes to paper towels to drain; set aside. Repeat cooking in batches, using another 3 tablespoons of the oil and the remaining potatoes.
For spinach filling, in a large skillet heat the remaining 1 tablespoon oil over medium-high heat. Add mushrooms and onion; cook and stir for 6 to 8 minutes or until tender. Stir in dill. Add spinach, artichokes, salt, and pepper; cook and stir over medium heat for 3 to 4 minutes or until spinach wilts. Using a fine-mesh strainer, drain spinach mixture, pressing down with the back of a wooden spoon to release any liquid. In a large bowl combine eggs, ricotta cheese, spreadable cheese, and lemon peel. Stir in spinach mixture. Set aside.
Preheat oven to 375 degrees F. Generously coat a 9-inch springform pan with cooking spray. Place springform pan in a foil-lined 15x10x1-inch baking pan. Cover the bottom of the springform pan with potato rounds, overlapping as necessary and making sure that there are no empty spaces. Arrange some of the potato rounds around the sides of the pan. Pour spinach filling into the pan.
Bake about 1 hour or until filling is set. Remove pan from oven; transfer to a wire rack. Let stand for 15 minutes. Working quickly, gently run a sharp knife between the edges of the springform pan and the potatoes. Release the sides of the springform pan and carefully lift to remove sides of pan.
Cut torte into wedges. If desired, garnish with halved grape tomatoes.