Begin by preheating your oven to 375°F (190°C). Line a 15x10-inch jelly roll pan with parchment paper, ensuring there is an overhang on the sides for easy removal later. Lightly grease the parchment paper.
In a medium mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, ground cinnamon, ground nutmeg, ground ginger, and salt until well combined. Set this dry mixture aside.
In a large mixing bowl, use an electric mixer on medium speed to beat the eggs and granulated sugar together until the mixture becomes thick and pale in color, about 3-5 minutes.
Slowly drizzle in the vegetable oil and add the vanilla extract while continuing to mix until well incorporated.
Gently fold in the finely grated carrots and the thoroughly drained crushed pineapple until evenly distributed.
Carefully add the dry ingredient mixture to the wet ingredients, folding gently until just combined. Be careful not to overmix to keep the texture light.
Pour the cake batter into the prepared jelly roll pan, spreading it evenly to cover the entire surface.
Bake in the preheated oven for approximately 15-20 minutes, or until a toothpick inserted into the center comes out clean.
While the cake is baking, prepare a clean kitchen towel by generously dusting it with powdered sugar.
Once the cake is baked, remove it from the oven and promptly invert it onto the prepared towel. Carefully remove the parchment paper. Starting from one short end, roll the cake tightly with the towel, forming a log shape, and allow it to cool completely in this rolled position, about 30 minutes.
In a mixing bowl, combine the softened cream cheese, powdered sugar, and fresh lemon juice. Beat until the mixture is smooth and creamy.
Once the cake has cooled, gently unroll it from the towel. Spread the cream cheese filling evenly over the surface of the cake.
Carefully re-roll the cake without the towel, ensuring the seam side is at the bottom. Wrap the rolled cake in plastic wrap and refrigerate for at least 1 hour to set the filling.
To serve, slice the chilled roll into pieces and, if desired, garnish with chopped pecans or walnuts for added crunch and flavor.