Rinse and scrub the sweet potatoes. Place them in a large stockpot, cover with cold water and 3 tablespoons of the kosher salt. Cook over medium heat until the potatoes are very tender, about 45 to 50 minutes. Cooking time will vary depending on the size of the potatoes.
Remove the potatoes and set aside until they are cool. When they are cool enough to handle remove the skins and place the peeled potatoes in a large mixing bowl.
While the potatoes are cooling, whisk together both the sugars along with the nutmeg and cinnamon. In a separate bowl, whisk the egg with the half and half, until they are well blended.
Beat the potatoes, starting on low speed, raising to medium, beating until they are fairly smooth. Add the melted butter along with the egg and half and half. Mix in on medium speed until well blended.
Add the sugar and spice mixture and the black pepper. Check for seasoning and the remaining 1 teaspoon kosher salt, starting with ½ teaspoon as needed to taste. (Check the flavors of the sweet potatoes before adding all the salt. The potatoes will be somewhat seasoned from the salted cooking water.)
Scoop the sweet potatoes into a baking dish that has been lightly sprayed with a cooking spray. (I use an oval dish that measures 12-¼ " x 8-¾ " x 2" deep.)
Bake the dish at 350-degrees for 35 to 40 minutes or until the sweet potatoes are heated throughout and the top is starting to deepen in color.Cooking will vary depending on the moisture in your potatoes.