Preheat oven to 350°F. Place whole unpeeled sweet potatoes on a foil-lined baking sheet. Roast for 1 ½ hours, until very soft. Cool slightly, then peel while warm.
Mix or process the sweet potatoes until smooth, stopping often to clean away strings. Use the tool that works best for you, whether that is a hand mixer, stand mixer, or food processor.
Mix in the butter until fully incorporated.
Add the evaporated milk, sugar, cinnamon, nutmeg, allspice, lemon juice, lemon extract, and vanilla extract. Mix until smooth and uniform.
Lightly beat the eggs in a separate bowl. Add them last and mix gently, just until combined. The filling should be thick but still easy to pour.
Fill the pie shells to about ¼ inch below the rim. Tap filled shells lightly or skim any surface foam if needed.
Bake at 350°F for 45 to 55 minutes. Start checking at 40 minutes. The pies are done when the edges are set and the centers still have a slight jiggle. Tent crusts with foil after about 30 minutes if browning too fast.
Turn the oven off and crack the door open a few inches. Leave the pies inside for 1 hour.
Move to a wire rack and cool at room temperature for 2 to 3 hours before refrigerating.