To make the cake layer:

1. Prepare an 8-inch cake pan with a parchment paper circle in the bottom and grease the sides. Preheat oven to 325°F (176°C).
2. Combine the flour, baking powder and salt in a medium sized bowl and set aside.
3. Add the butter, sugar, oil and vanilla extract to a large mixer bowl and beat together until light in color and fluffy, about 2-3 minutes. Do not skimp on the creaming time.
4. Add the eggs one at a time, mixing until mostly combined after each. Scrape down the sides of the bowl as needed to be sure all ingredients are well incorporated.
5. Add half of the dry ingredients to the batter and mix until mostly combined.
6. Slowly add the milk and mix until well combined. The batter will look curdled, but that’s ok.
7. Add the remaining dry ingredients and mix until well combined and smooth. Scrape down the sides of the bowl as needed to be sure all ingredients are well incorporated. Do not over mix the batter.
8. Pour the batter evenly into the prepared cake pan and bake for 30-35 minutes, or until a toothpick comes out with a few crumbs.
9. Remove the cakes from the oven and allow to cool for about 2-3 minutes, then remove to cooling racks to cool completely.

To make the strawberry filling:

1. To make the strawberry filling, add the strawberries to a food processor or blender and puree until smooth. You should have about 1 1/2 cups of puree. Strain it through a fine mesh strainer to remove the seeds, if desired.
2. Add the puree to a medium sized saucepan and cook over medium heat. Allow the mixture to come to a slow boil, stirring consistently to keep it from burning, until it has thickened and reduced to 3/4 cup, about 20-25 minutes. To measure, pour the puree into a measuring cup. If it’s more than 3/4 cup, add it back to the pan and continue cooking.
3. When the puree has thickened and reduced, combine the heavy cream, sugar and cornstarch and whisk together. Pour the cream mixture into the strawberry reduction and gently whisk to combine. Continue to heat over medium heat until the mixture comes to a gentle boil. Boil for 45 seconds to 1 minute, or until it looks like it’s thickened nicely. It will continue to thicken as it cools, so you don’t want it to thicken too much.
4. Remove from mixture from heat, pour into a heat proof bowl and allow to cool to at least room temperature (or refrigerate it to cool it more quickly). If you’re making it ahead, you can press clear wrap onto the top of the mixture and place it in the fridge for 2-3 days.

To build the cake:

1. Set your ice cream out for 15-20 minutes before you need it to let it soften, but not melt. I like to scoop it out into lots of smaller scoops so that it can soften more evenly.
2. Line your 8-inch pan with two pieces of clear wrap, one on top of the other going in opposite directions. The pieces of clear wrap should be long enough that you can use them later to lift the cake out of the pan. Press the clear wrap into the pan and press against the bottom and sides to flatten it.
3. Once the ice cream has softened, stir until creamy and smooth, then pour the ice cream into the lined pan and spread it into an even layer.
4. Add the cooled strawberry mixture to the top of the ice cream and spread into an even layer. Place the pan in the freezer for 15 minutes or so for things to firm up a bit.
5. If your vanilla cake layer isn’t flat, use a large serrated nice to trim off the dome. Place the cake on top of the strawberry layer, with the trimmed side down on the strawberry layer. Use the excess clear wrap to wrap around the cake and place in the freezer for 3-4 hours or until completely firm.

To finish the cake:

1. When the cake is frozen and firm, use the clear wrap to loosen and lift the cake out of the pan. Turn it over onto a cardboard cake circle or a serving platter. Remove the clear wrap from the top of the ice cream.
2. To make the whipped cream frosting, add the heavy whipping cream, powdered sugar and vanilla extract to a large mixer bowl and whip on high speed until stiff peaks form.
3. Frost the cake with the whipped cream, working quickly so that the ice cream doesn’t melt, then decorate as desired. I added some strawberry slices to the outside bottom of the cake, then colored the remaining whipped cream with some pink and red gel icing color and piped on a top and bottom border.
4. Store the cake in the freezer until ready to serve. If you have room in your freezer, store it in an air tight container. The cake is best if eaten within a week or so.