Preheat oven to 425° F. Place puff pastry sheets side by side on a large baking sheet. Pinch the two sheets together at the center seam to form one large sheet. Use a fork to poke holes evenly over entire sheet. (If any excess pastry hangs over the sheet, roll it to form a crust.) Par-bake the pastry for 10 minutes.
Meanwhile, cook shallots with olive oil in a medium skillet on medium-high heat for 5 minutes, stirring often.
When pastry has par-baked, sprinkle it evenly with the shallots, tomatoes, prosciutto, gorgonzola cheese and goat cheese. Bake for an additional 10-15 minutes or until pastry is golden and cheese is bubbling.
Meanwhile, whisk the balsamic vinegar, Dijon mustard and honey together in a small bowl. Set aside.
When pizza is done cooking, remove it from the oven, drizzle it with the balsamic mixture and sprinkle with basil. Slice and serve.