Preheat the oven to 350 degrees.
Heat 2 tablespoons olive oil in a heavy saucepan or Dutch oven over medium-high heat. Add the squash and saute until tender, 15 to 20 minutes. Remove the squash and set aside.
Return the saucepan to the stove over medium heat and the remaining 2 tablespoons olive oil. Add the onions and saute 15 minutes, until light brown. Add the vinegar and maple syrup and stir every few minutes until thick and reduced, 15 to 30 minutes.
Add the onion mixture to the squash and mash lightly, leaving some chunks. Add the red pepper flakes and season to taste with salt. Set aside.
Roll the pizza dough out onto a pizza stone or baking sheet in an even layer. Spread the butternut squash mixture evenly across the dough, then sprinkle with Boursin cheese. Add the ground turkey, if desired.
Bake 15 minutes, until the crust is cooked through. Dress with arugula and let wilt, then drizzle with balsamic vinegar before slicing and serving.