Preheat oven to 350°F. Grease your baking pan and line with parchment paper.
In your mixer, whisk together sugar, oil, butter, and vanilla until well combined.
Add two eggs, plus the yolk from the third, and combine.
Add in the buttermilk and combine.
Add in the baking powder, baking soda, and salt, and combine.
Sift in the flour and mix until almost, but not quite, smooth.
Pour your batter into your pan. Bake for 30-35 minutes, or until a knife or toothpick comes out clean but moist.
Move your cake to a cooling rack to cool and use your spoon handle or dowel to poke holes in the cake. I like a wooden spoon for this.
Carefully pour most of the strawberry puree in the holes and over the top of the cake, reserving a couple of tablespoons (3-4) for the finishing touch.
Put the cake in the fridge to chill for 2-3 hours.