Puree 1 pound of strawberries in a food processor. Add to a saucepan and heat for 30 minutes over medium heat. It should reduce to about ½ cup. Let cool to room temperature.
Preheat oven to 350°F and prepare two 9" round cake pans. Line the bottoms with parchment paper and then butter the pans. Toss a tablespoon of flour in the pans and turn to coat the entire pan, tossing the extra flour out. Set aside.
In a medium bowl, whisk together the flour, baking powder and salt. Set aside.
In the bowl of a stand mixer, cream together the sugar, butter and oil until light and fluffy, about 2 minutes. Beat in the egg whites on high speed until combined, about another 2 minutes. Add the Greek yogurt and vanilla and beat until combined. You can also use a hand mixer to do this.
With the mixer on low speed, add the dry ingredients and mix until just incorporated. Add ½ cup of the milk and mix until just combined.
Now divide the batter evenly between two bowls. In one bowl, stir in the remaining ½ cup of milk until combined. In the other bowl, stir in the strawberry puree and 1-2 drops of red food coloring if desired.
Divide the batter between the two cake pans. Bake for 30-35 minutes or until the tops are set and no longer wiggly. Inserting a toothpick should come out mostly clean with some moist crumbs, but no wet batter. Remove and let cool for 10 minutes and then run a knife around the edges of the pan. Invert on a cooling rack and allow to cool completely before frosting.