Preheat the oven to 350°F. Grease and flour three 6-inch cake pans and set aside.
In a large mixing bowl, whisk together the flour, sugar, baking powder, and salt.
In a separate bowl or large measuring cup, whisk together the milk and eggs. Pour in the butter, oil, and vanilla. Using a hand mixer or whisk, blend the wet ingredients into the dry ingredients. Finish by folding together with a rubber spatula until smooth.
Tip the mixture into the prepared pans. Bake for 25 to 30 minutes or until a toothpick inserted comes out clean or with a few moist crumbs. Completely cool the cake before frosting.
To Make the Strawberry Filling and Buttercream
Puree the diced strawberries in a mini food processor or blender. Pour into a saucepan along with the granulated sugar and salt. Cook to simmer then reduce the heat to low.
Continue to cook to reduce the sauce and make the flavor more concentrated, about 15 minutes. Do not reduce to less than 1 cup of puree.
Make a slurry by whisking the cornstarch with a couple teaspoons water until dissolved. Pour the slurry into the strawberry sauce. Add a squeeze of a ½ lemon and stir to combine. Keep stirring the sauce until it thickens then remove from the heat to cool completely.
When ready, use an electric mixer to mix the butter until smooth. Add the powdered sugar and mix on low speed until combined.
Add about 4 tablespoons strawberry sauce. Mix to combine.
To Assemble
Place one layer of cake on cake board or serving dish. Fill a piping bag with a plain tip with strawberry buttercream.
Pipe a ring of buttercream around the outer edge of the cake, about ½-inch tall. Fill the center with buttercream and spread with the back of a spoon to create a shallow bowl.
Dollop 2 to 3 tablespoons strawberry sauce and gently swirl to combine, making sure none of the sauce reaches the edges of the cake. Top with the next layer and repeat.
Cover the cake with a thin layer of buttercream all over. Chill the cake for 15 minutes or until firm.
Smoothly ice the cake with buttercream frosting. Use any remaining frosting to decorate. Add fresh strawberries, if desired.
Notes
Serve this strawberry vanilla cake at room temperature. Keep at a cool room temperature over night.Store leftovers covered in plastic in the refrigerator for up to 4 days.Always make sure to use a buttercream dam to hold in loose fillings like jam. Consequently, if the strawberry sauce begins to leak out as you stack the cakes, scrape it out and start again with a buttercream dam.If the buttercream is too soft to pipe, add in a bit more powdered sugar - a ½ cup at a time. If it is too stiff, add a bit more strawberry sauce - a tablespoon at a time.