Heat the oven to 400°F.
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 let sit at room temperature until cool enough to handle, about 30 minutes. Meanwhile, reduce the oven temperature to 350°F.
Peel off the skin from the potatoes and discard it. Weigh the sweet potato flesh; you should have between 12 and 13 1/2 ounces (340 and 380 grams). Transfer the sweet potato flesh to a stand mixer fitted with the paddle attachment. Beat on medium-high speed until smooth, about 1 minute. Turn the mixer off, then add the sugar, cinnamon, nutmeg, and salt. Return the mixer to medium-high and continue to beat until smooth, about 30 seconds. Scrape down the paddle and sides and bottom of the bowl, then add the cream and eggs. Beat on low speed until well-combined, about 1 minute.
Place a large 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 smooth 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. Let cool on a wire rack for at least 1 hour. Serve at room temp or chill completely before slicing. Stash any leftovers in the refrigerator.