1. Preheat oven to 350°F.
2. Grease or butter one 2 quart casserole dish.
3. In a large stockpot, cover sweet potatoes with 1 inch of water; boil for 20 minutes or until fork tender. Drain, allow to cool and remove skins.
4. Place potatoes in a mixing bowl and with an electric mixer, (or “rice” the potatoes) beat on low speed until potatoes begin to break up. Increase speed to medium high and blend until smooth.
5. Reduce speed to low and add white and brown sugars, cream, butter, vanilla, sweet vermouth,eggs and salt. Mix well.
6. Allow any potato “fibers” to remain on the beater and remove.
7. Pour sweet potato mixture into the casserole dish.
8. Prepare the topping in a small bowl by whisking together the 1 cup dark brown sugar, flour, butter and pecans.
9. Sprinkle mixture over potato mixture and bake for 40 minutes.