Preheat the oven to 350°F (175°C). Grease and flour three 9-inch round cake pans.
In a large mixing bowl, whisk together the flour, sugar, cocoa powder, baking powder, and salt until well combined.
In another bowl, mix the milk, vegetable oil, eggs, and vanilla extract. Gradually add the wet ingredients to the dry ingredients, mixing until just combined.
Divide the batter evenly into three bowls. Leave one bowl as is for the chocolate layer. Add strawberry puree to the second bowl and mix until combined. For the third bowl, you can add a few drops of food coloring if you want a more vibrant pink color for the strawberry layer.
Pour the chocolate batter into one prepared cake pan, the strawberry batter into the second, and the plain vanilla batter into the third. Bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean.
Once baked, allow the cakes to cool in the pans for 10 minutes before transferring them to wire racks to cool completely.
While the cakes cool, prepare the whipped cream. In a mixing bowl, beat the heavy cream, powdered sugar, and vanilla extract until soft peaks form.
Once the cakes are completely cool, place the chocolate layer on a serving plate. Spread a layer of whipped cream on top, then add the strawberry layer. Repeat with more whipped cream and top with the vanilla layer.
Frost the top and sides of the cake with the remaining whipped cream. Garnish with chocolate shavings or sprinkles.