Preheat the oven to 400 degrees F (200 degrees C). Prick sweet potatoes several times with a fork and place onto a baking sheet.
Bake in the preheated oven until sweet potatoes are easily pierced with a knife, 50 minutes to 1 hour. Remove from the oven and allow to rest, 8 hours to overnight.
Preheat the oven to 375 degrees F (190 degrees C).
Combine graham crackers, walnuts, sugar, nutmeg, and cinnamon in a food processor and blend until crumbly. Incorporate melted butter. Press mixture evenly into a 9-inch springform pan to form a crust.
Bake in the preheated oven until golden brown, about 10 minutes. Remove from oven and reduce temperature to 300 degrees F (150 degrees C). Let crust cool.
Place a cake pan filled with water on the bottom rack of the oven to create moisture and prevent cheesecake from cracking.
Combine baked sweet potatoes, cream cheese, white sugar, brown sugar, lemon extract, vanilla extract, nutmeg, and cinnamon in a high-powered blender (such as Vitamix®) and process until smooth. Mix in whole eggs andegg yolks on the lowest speed possible; be careful not to overmix filling.
Pour filling into crust.
Bake in the preheated oven until a tester comes out clean and cheesecake just jiggles slightly in the center, about 1 hour and 25 minutes. Leave cheesecake in the oven with the door ajar to allow cheesecake to cool gradually and prevent cracking, about 45 minutes.
Refrigerate cooled cheesecake for 2 hours before serving.
If you don’t have the time or lack the patience, feel free to bake the sweet potatoes the same day until you can insert a knife through the center of the potato, about 1 hour at 400 degrees F (200 degrees C).
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