Make the za'atar focaccia bread. Combine 1 cup warm water with 1 teaspoon sugar and 1 tablespoon active dry yeast. Let sit for 5 minutes or until the mixture is foamy.
Mix the yeast mixture with 2 ½ cups all-purpose flour, 1 teaspoon salt, and 2 tablespoon olive oil. Knead the dough until smooth, about 5-7 minutes. Cover and proof until double in size, about 1 hour.
Punch down the dough. Pour 2 tablespoon in a quarter baking sheet pan (9x13 inches) and transfer the dough to the pan. Gently spread the dough to fill the pan. Use your fingers and make indentations in the dough. Drizzle the remaining 2 tablespoon olive oil on top and sprinkle with 1 tablespoon za'atar seasoning. Let rest for 20 minutes.
Preheat oven to 400 degrees F.
Bake the focaccia bread for 20-25 minutes or until golden brown. Remove from oven and cool.
Make the roasted red pepper sauce. Increase the oven temperature to 425 degrees F. Roast 2 bell peppers until softened and slightly blackened, about 12-15 minutes. Remove from the oven and place the bell peppers in a bowl. Cover the bowl with plastic wrap and let sit for 10 minutes. Remove the wrap and peel the blackened skin off the bell peppers.
Blend the roasted peppers with ¼ cup olive oil, 1 teaspoon garlic, the juice of ½ lemon, and ¼ cup toasted walnuts. Season with salt and pepper. Set aside.
Make the lemony olive tapenade. Blend together all of the ingredients including ½ cup green olives, 1 tablespoon capers, ¼ cup parsley, the juice of 1 lemon, ¼ cup olive oil, and 1 teaspoon minced garlic. Season with salt and pepper.
Assemble the sandwiches. Slice the focaccia bread in half vertically. Spread the red pepper sauce on the bottom bread and top with arugula, prosciutto, salami, mozzarella, and olive tapenade. Top with the remaining bread. Serve.