Place oven rack in lowest position; preheat oven to 450 degrees F. Lightly coat a large baking sheet with nonstick cooking spray; set aside (or line with parchment paper that is safe to 450 degrees F).
To caramelize onions, in a large skillet melt butter over medium-low heat. Add onion. Cook, covered, about 12 minutes or just until tender, stirring occasionally. Uncover; cook and stir over medium-high heat for 3 to 5 minutes more or until very tender. Remove from heat; set aside.
On a lightly floured surface, roll out or press pizza dough into an irregular rectangular shape, about 13x9 inches. Transfer to prepared pan. Build up edges slightly. Prick generously with a fork. Bake until puffed and lightly crisped on the bottom, about 8 minutes.
Top with ham, caramelized onion, apple and cheese. Bake 10 minutes more or until crust is crispy and golden and the cheese is melted. Sprinkle with fresh thyme, if desired. Season to taste with salt and pepper.