Preheat the oven to 400 degrees F with an oven rack in the center position.
Place the sweet potatoes on a quarter sheet pan or baking dish and roast until fork-tender, about 1 hour. Transfer to a plate and cool to room temperature, about 30 minutes. Meanwhile, reduce the oven temperature to 350 degrees F.
Peel the sweet potatoes and discard skin. Weigh the sweet potato flesh. You should have between 340 and 380 grams (12 to 13 1/2 ounces).
Transfer sweet potatoes to bowl of stand mixer and beat with the paddle on medium-high speed until smooth, about 1 minute. Kill the mixer, add the sugar, cinnamon, nutmeg, and salt, and beat on medium-high until smooth, about 30 seconds. Turn off the mixer and scrape down the paddle and bowl. Add the cream and eggs, then beat on low speed until well-combined, about 1 minute.
Place a fine-mesh sieve over a medium bowl, then pour the sweet potato mixture through the sieve. Use a rubber spatula to press the filling through the sieve and strain out any sweet potato fibers; it will take some effort but is well worth it for a silky pie. Transfer to the pie crust and smooth the top.
Bake until the pie just jiggles slightly in the center and has reached an internal temperature of 165 to 175 degrees F, 40 to 45 minutes. Cool on a wire rack for at least 1 hour. Serve at room temp or chill completely before slicing. Refrigerate any leftovers.