Preheat your oven to 350°F (175°C). Grease the 9x13 inch baking pan or line with parchment paper for easy removal.
In a large mixing bowl, combine the sweet potato puree, granulated sugar, brown sugar, vegetable oil, eggs, and vanilla extract. Whisk until the mixture is smooth and well-blended.
In a medium mixing bowl, mix the flour, baking powder, baking soda, salt, ground cinnamon, and chopped nuts (if using).
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Do not overmix.
Pour half of the batter into the prepared baking pan, spreading it evenly.
In a small bowl, mix together ¼ cup sugar with 1 teaspoon of cinnamon. Sprinkle this mixture over the first layer of batter.
Pour the remaining batter over the sugar and cinnamon layer.
Swirl a knife through the batter to create a marbled effect, being careful not to mix it too much.
Bake in the preheated oven for 45 minutes, or until a toothpick inserted in the center comes out clean.
While the cake is baking, prepare the glaze by whisking together powdered sugar, milk, and vanilla extract in a small bowl until smooth.
Once the cake is done, allow it to cool in the pan for about 10-15 minutes, then transfer it to a cooling rack.
Drizzle the glaze over the warm cake and let it cool completely before serving.