Place sweet potatoes in a large saucepan and cover with cold water by 2 inches. Salt generously. Bring to a boil, then reduce heat to a simmer and cook until sweet potatoes are easily pierced with the tip of a paring knife, 15-20 minutes.
Meanwhile, combine egg whites, sugar, and salt in the heatproof bowl of a stand mixer set over a pan of simmering water. Whisk constantly by hand until mixture is warm to the touch and sugar has dissolved (the mixture should feel completely smooth when rubbed between your fingertips).
Attach the bowl to a mixer fitted with the whisk attachment. Starting on low and gradually increasing to medium-high speed, whisk until stiff, but not dry, peaks form. Continue mixing until meringue is fluffy and glossy and completely cool (test by touching the bottom of the bowl), 10-15 minutes. Add vanilla and pumpkin pie spice and mix on low just until combined. Transfer meringue to a disposable piping bag fitted with a 1A Wilton decorating tip and set aside.
When sweet potatoes have finished cooking, drain, then return to pan. Heat over medium, stirring, until any remaining liquid has evaporated and a thin film covers bottom of pan, about 2 minutes.
Remove pan from heat. Add milk and butter and mash until smooth. Season to taste with salt and pepper. Transfer mashed sweet potatoes to a buttered 8x8” square baking dish. Using the meringue, pipe a checkerboard pattern onto the potatoes. Toast meringue with a kitchen torch, or place under a broiler, until peaks are toasted and golden and serve.