Cut peppers into thin strips; slice green onions.
Melt butter in a 10-inch cast-iron skillet over medium-high heat; add peppers and green onions, and cook, stirring constantly, until tender. Remove from skillet; wipe drippings from skillet, and set aside to cool.
Unroll pizza dough, stretching to a 14 1/2-inch square (do not tear dough). Gently place dough in cooled skillet, allowing edges to overhang. Place ham, pepper mixture, salad dressing, and cheese on dough; bring corners and sides of dough over cheese. Twist corners together in center, forming a knot; pinch seams to seal.
Bake at 425° for 15 to 20 minutes or until browned. Let stand 5 minutes before cutting into wedges.