Preheat the oven to 350°F. Grease and line a 9X13-inch baking pan with parchment paper. Set aside.
Whisk together the flour, cornstarch, baking powder, baking soda and salt in a medium bowl and set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl with a hand mixer), beat the butter and sugar together on medium speed until light and fluffy, 3 to 4 minutes. Add the oil and mix to combine. Stop the mixer and scrape down the sides of the bowl.
With the mixer on medium-low speed, add in the vanilla and eggs, one at a time allowing each to combine before adding the next. Stop the mixer and scrape down the sides of the bowl.
Add about half of the dry ingredients and mix on low speed until incorporated. Stream in the milk, followed by the strawberry purée and a few drops of food coloring, and mix until the liquids are absorbed. Add the remaining dry ingredients and mix until combined. Mix on low speed no more than 30 seconds.
Pour the batter into the prepared pan and smooth out with a spatula. Bake for 30 to 34 minutes or until a toothpick inserted into the center comes out clean or with a few moist crumbs.