Cover 2 cookie sheets with lavosh. Drizzle lavosh with little extra-virgin olive oil and turn over. Layer cheese on the lavosh. If you are substituting smoked white cheddar, scatter the shredded cheese in an even layer allowing a little of the lavosh to still peek through.
Place bread in oven to melt cheese, 5 minutes. Cut lavosh into squares and dot each square with small ham strips, draping them over the cheese. Scatter chopped greens over pizza squares. Drizzle pizza squares with extra-virgin olive oil and season with black pepper. Transfer to plate and serve.
*If your market does not sell this, substiutute 3/4 pound smoked white cheddar, shredded