Step 1Fill a medium saucepan with water and bring it to a boil over high heat. Wash the spinach well in several changes of water and drain. Place the leaves in the saucepan, cover and cook over high heat until wilted, 15 to 20 seconds. Drain well, squeeze dry and coarsely chop. Press the spinach between paper towels to drain any additional moisture. Set aside.
Step 2Heat 2 teaspoons olive oil in a heavy-bottomed 9-inch saute pan over medium heat. Add the zucchini and garlic, and season with salt and pepper to taste. Cook, stirring constantly, until soft and starting to brown. Transfer to a small bowl.
Step 3Heat 2 1/2 teaspoons oil in the pan over medium heat. Add the shiitakes and season with salt and pepper to taste. Cook until soft, then transfer to a small bowl. Wipe the pan clean.
Step 4Beat 2 eggs in a medium bowl with salt and pepper to taste. Add the cooked spinach and mix well. Heat 1 teaspoon olive oil in the saute pan over medium heat. When it shimmers, add the egg mixture and cook, stirring and lifting to make a puffy, open-faced omelet; the eggs should be set but still moist on the top. Slide onto a 10-inch serving plate, moist side up.
Step 5Beat 2 more eggs in a bowl and season with pepper only, then stir in the anchovies. Heat 1 teaspoon oil in the pan, cook the egg mixture like the spinach omelet and lay onto the spinach omelet.
Step 6Repeat with 2 more eggs and the shiitakes. This layer will not need additional seasoning.
Step 7Repeat with 2 more eggs, pepper only and the tapenade.
Step 8Repeat with 2 more eggs, salt and pepper and the piquillos.
Step 9Repeat with 2 more eggs and the zucchini. This layer will not need additional seasoning.
Step 10Repeat with 2 more eggs and the capers.
Step 11Repeat with 2 more eggs, salt and pepper and the sun-dried tomatoes.
Step 12Repeat with 2 more eggs, pepper only and the pesto, but carefully flip and slide this omelet onto the stack moist side down.
Step 13If serving immediately, cut the crespeou into wedges. Otherwise, weigh down several hours before slicing.