Position racks in the middle and lower third of the oven and put an inverted baking sheet or pizza stone on the middle rack; preheat to 475 degrees F. Toss the squash, olive oil, honey, vinegar, red pepper flakes and 1/2 teaspoon salt on another baking sheet; spread in a single layer. Bake on the lower rack until lightly browned and tender, about 10 minutes.
Stretch the dough into a 12-by-16-inch rectangle on a floured surface; transfer to a piece of parchment paper. Top with the roasted squash, sage, cheese and soppressata. Slide the pizza (on the parchment) onto the hot baking sheet or pizza stone. Bake until the cheese is bubbling and the crust is golden, 10 to 12 minutes. Transfer to a cutting board; top with the parsley, drizzle with olive oil and cut into pieces.