In a small saucepan over medium-low heat, simmer the puréed strawberries until reduced by half. Set aside to cool to room temperature.
Preheat the oven to 350ºF (180ºC). Line the bottom of an 8-inch round cake pan*** with parchment paper. Grease and flour the inside.
In a medium bowl, whisk together the flour, baking powder, baking soda and salt.
In a large bowl, beat the sugar, oil, egg, egg white, and extracts, with an electric mixer at medium speed, until smooth. Alternately, you can whisk the mixture together by hand until smooth. Stir in 1/3 cup of the cooled strawberry reduction and the food coloring. (Reserve the remaining strawberry reduction for the icing.)
Stir the flour mixture into the batter, in 2 additions, alternating with the sour cream. Mix just until combined. Transfer the batter to the cake pan.
Pipe the strawberry swirl mixture onto the batter in a spiral pattern. Bake until a toothpick inserted into the center of the cake comes out clean, about 25-30 minutes.
Let the cake cool in the pan for 10 minutes, then transfer it to a cooling rack.