Preheat the oven to 375F/190C. Spray a large casserole dish with non-stick baking spray and set aside.
Peel the potatoes, then cut them into large chunks. Place into a pot filled with water and bring to boil over high heat. Boil the potatoes for about 20 to 25 minutes (timing depends on the size), until the potatoes are very soft. Drain the water and place the potatoes into a large mixing bowl.
To the potatoes, add the softened butter, sugar, salt and vanilla. Using a mixer or a potato masher, puree the potatoes until they’re smooth. Next, add in the eggs and egg yolks and mix again for another minute. Transfer the sweet potato puree into the casserole and level off the top.
Brown Sugar Pecan Topping:
While the sweet potatoes are cooking, prepare the brown sugar and pecan topping. Place the flour into a medium-sized mixing bowl. Cube the cold butter and add it to the flour, then use a pastry blender or 2 large forks to cut the butter into the flour until the mixture resembles large crumbs.
Next, add in the brown sugar, cinnamon and nutmeg. Using your fingers, blend the brown sugar into the butter and flour. Last, stir in the pecans. Spread this topping evenly over the sweet potato layer.
Bake the sweet potato casserole at 375F/190C for 25 to 27 minutes, until the topping is caramelized and golden brown.
While the casserole is baking, prepare the marshmallow meringue topping. Into a very clean mixing bowl, add the egg whites and whisk on high speed for a minute until soft peaks form. In a small saucepan, add the sugar and water but do not stir! Attach a candy thermometer to the side of the pan and cook the syrup over medium-high heat for 5 to 6 minutes, until the syrup reaches 240F/115C. Do not stir the syrup as it cooks!
Immediately after the syrup as reached temperature, turn the mixer on to medium speed and pour the hot syrup into the egg whites in a slow and steady stream. Add in the lemon juice, then turn the mixer up to high speed and continue whisking for 7 to 9 minutes. The meringue should form stiff peaks and be glossy and fluffy.
Once the casserole is done baking, add the prepared meringue on top. Using a kitchen torch, torch the meringue to caramelize it. Alternatively, place the casserole under the broiler for a few minutes. Enjoy the casserole warm.