Whisk flour, baking soda, baking powder, salt and pudding mix in a mixing bowl.
Puree strawberries in a food processor, leaving a few small chunks.
Whisk starter, buttermilk, and 1 cup of the puree in another bowl. Reserve any excess puree for frosting.
In a large bowl, beat butter and sugar with an electric mixer on medium speed until light and fluffy. Add the eggs one at a time, making sure that each one is fully incorporated before adding the next. Add vanilla and lime zest.
Reduce speed to low and alternate adding the starter mixture and the flour mixture until flour is incorporated.
Divide batter into prepared cake tins.
Bake for 35-40 minutes or until the bread loosens evenly from the sides and a toothpick inserted in the center of the bread comes out clean.
Allow to cool completely before frosting.
Use the wrappers from the sticks of butter to grease the cake tins.