Rinse the sweet potatoes but don't peel them, and halve them only if they're too large to fit in the pot. Place in a large pot with 1 teaspoon of the salt and enough water to cover them by 1 inch. Boil the sweet potatoes until tender enough to be easily pierced with a skewer, 15 to 35 minutes. Drain them in a colander in the sink.
While the potatoes cool slightly, combine the butter, brown sugar, cream, vanilla, and remaining 1/2 teaspoon salt in a mixing bowl. Peel the warm potatoes (the jackets should slip right off), cut them into large chunks, and toss them in the bowl. Mash until the mixture is combined. Serve warm, garnished with pecan pieces (if using). The sweet potatoes may be refrigerated and reheated before serving.