Peel and dice sweet potatoes. Place in a large pot and cover with water. Bring water to a boil, reduce heat to medium and simmer until the potatoes are fork tender. (About 20 minutes.) Drain.
Place drained sweet potatoes back in large pot. Add the brown sugar, cinnamon, nutmeg, salt, butter and half the evaporated milk. Cook on low and mash with a potato masher. Simmer for about 5 minutes. Remove from heat and allow to cool a bit.
Using a stand mixer, combine remaining evaporated milk, sugar, eggs, and vanilla. Mix well. Add the sweet potato mixture and mix well.
Pour the filling into the pie crust. Place pie pan on a baking sheet and bake for 10 minutes at 375 degrees. Reduce the heat to 325 degrees and cook for an additional 45-50 minutes.