Preparation

• Preheat the oven to 500°F, with a rack in the upper third position. In a large bowl, combine the shallots and vinegar, then set aside. Grease an 18 x 13-inch sheet pan with oil, making sure you get into the corners. Put the dough on the pan and firmly push and stretch it with your fingers, letting it rest briefly every few pushes and stretches, until it covers the bottom of the pan in a relatively even layer. (Depending on the temperature and elasticity of your dough, it might not stretch as easily. Don’t  worry if it doesn’t completely reach the edges. Just fill the pan as much as you can.) Repair any holes by pinching the dough together.
• Brush the dough with the 2 Tbs. oil. Sprinkle the thyme evenly over the dough, press the leaves into it a bit, and season with salt and pepper. Bake the dough, rotating the pan halfway through, until golden brown on the bottom and the edges start to pull away from the sides of the pan, about 10 minutes.
• Meanwhile, to the bowl with the shallots and vinegar, add a splash of lemon juice and the remaining 3 Tbs. oil. Season with salt and pepper, then whisk together. Check the seasonings by quickly dipping in a piece of lettuce, shaking it off, and tasting. Top the dressing with the tomatoes, artichoke hearts, cucumbers, capers, lettuce, and tuna (if using) and set aside without tossing.
• When the crust is ready, transfer it to a cutting board. Toss the salad, check the seasonings, then mound it evenly over the crust, leaving a narrow border around the edges. Lay the prosciutto slices (if using) across the salad and scatter the feta over top. Cut the pizza salad and serve right away.