Preheat oven to 350°F (180°C). Line a jelly roll pan with parchment paper.
Sift flour, baking soda, cinnamon, nutmeg, and salt into a bowl.
Whisk eggs, oil, and vanilla until well blended.
Fold dry ingredients into wet mixture in three additions.
Gently stir in grated carrots.
Spread batter into prepared pan using a spatula.
Bake for 8–10 minutes until edges rise but center is still soft.
Place a clean, real towel or kitchen cloth over the warm cake.
Flip cake onto towel (parchment paper-side up), then remove paper.
Starting at one edge, roll towel and cake into a log. Let cool completely.
Beat cream cheese, butter, powdered sugar, and lemon juice until smooth.
Once cake is cold, unroll and sandwich with cream cheese filling.
Roll tightly, tucking in corners, then refrigerate for 1 hour before slicing.