Preheat the oven to 350 F and grease a 9 by 13 inch sheet pan.
Cream the butter and sugar until light, then beat in the eggs one at a time.
Mix in the sour cream and vanilla until smooth.
Whisk the flour, baking powder, baking soda, and salt in a separate bowl.
Add the dry ingredients to the wet mixture in two additions, mixing just until combined.
Fold in the strawberries and strawberry jam, if using.
Spread the batter into the pan and bake until a toothpick comes out clean, about 30 to 35 minutes.
Cool the cake completely before spreading on the frosting.
Beat the cream cheese, butter, powdered sugar, strawberry puree, and vanilla until fluffy.
Frost the cooled cake and chill briefly before slicing.