Preheat oven to 350°F (175°C). Line a 10x15-inch jelly roll pan with parchment paper and grease lightly.
Beat eggs and granulated sugar on high for 5–7 minutes until thick and pale. Add vanilla, oil, and milk, and mix until combined.
Whisk together flour, baking powder, and salt in a separate bowl. Gently fold into the wet mixture.
Divide batter into four bowls. Add pastel gel food coloring (pink, green, blue, yellow) to each. Spoon dollops onto the pan and swirl gently with a skewer or knife.
Bake for 10–12 minutes until the cake springs back when touched.
Immediately turn the cake onto a powdered sugar-dusted towel and remove the parchment paper. Roll it up gently, short end to short end, and let it cool completely.
Whip heavy cream, powdered sugar, and vanilla extract in a chilled bowl until stiff peaks form.
Unroll the cooled cake, spread whipped cream filling evenly, then re-roll the cake without the towel.
Frost with whipped cream and sprinkle with pastel sprinkles. Chill for 30 minutes before slicing.