Step 1: Preheat your oven to 400°F (200°C). Cut the butternut squash in half lengthwise, remove seeds, and place cut-side down on a baking sheet. Roast for 45-50 minutes until very tender. Let cool, scoop out the flesh, and puree in a food processor until smooth. Measure out 2 cups for the roasted butternut squash cake recipe.
Step 2: Lower the oven temperature to 350°F (175°C). Grease and flour a 9x13 inch baking pan or two 9-inch round cake pans.
Step 3: In a medium bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, nutmeg, and ginger. Set aside.
Step 4: In a large bowl, cream together the 1 cup of softened butter, granulated sugar, and brown sugar until light and fluffy. Add eggs one at a time, beating well after each addition. Stir in the vanilla extract and the 2 cups of squash puree.
Step 5: Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not over-mix.
Step 6: Pour the batter into the prepared pan(s) and smooth the top. Bake for 35-45 minutes, or until a toothpick inserted into the center comes out clean.
Step 7: Allow the cake to cool completely on a wire rack. While cooling, prepare the frosting by beating the cream cheese and butter together until smooth, then gradually adding powdered sugar and vanilla until fluffy.
Step 8: Frost the cooled cake and serve. Store any leftovers in an airtight container.