Chop and toss squash, potatoes, and carrots in olive oil. Spread into skillet and bake at 425 for about 20 minutes (until veggies are almost or just barely tender).
Remove from the oven and push veggies to the perimeter of the skillet (leaving a decent sized space in the center). Turn stovetop to medium heat and add butter into the center of the pan (dice up so it melts evenly).
Bring butter to a simmer and then whisk in flour until combined and sludgy (this happens quick)! Once sludgy, pour in broth and add onion, salt/pepper, and rosemary.
Stir to combine and return to a simmer to thicken the mixture, stirring occasionally.
Once thickened, turn off heat and fold in the turkey.
Defrost/unroll pie crust and place over the top of the entire skillet, pinching the edges in a bit to create a ridge around the perimeter of the pan. Stab the center a couple times and brush over the crust with a thin layer of whisked egg.
Throw the whole pan in the oven and bake at 375 for about 20 minutes (until your crust is golden)!