In a large mixing bowl, combine dry ingredients and set aside.
In a small saucepan over low heat (or large bowl in microwave) LIGHTLY warm water, buttermilk and olive oil. Making sure liquid is not hot to avoid curdling, add egg, mix well with wire whisk.
Stir wet mixture into dry mixture, whisk well for 3 minutes or so.
Using a wooden spoon or rubber spatula, stir in additional flour a little at a time until all combined.
Cover bowl with towel or greased plastic wrap, set in warm place and allow dough to rise until doubled in size, about 1 hour.
Preheat oven to 176C/350F.
Once dough has doubled, using floured hands, turn out onto a floured surface. Quarter dough and place each quarter in greased kulich or panettone paper molds or baking tins. Dough will be sticky, it's normal. See notes. Top with additional spoonful of pesto before baking, save some for serving.
Bake for 30-40 minutes or until golden brown. Allow loaves to cool 20 minutes or so, remove wrappers and cool a few more minutes on wire rack. See notes.
Once loaves are fully cooled and ready to serve, top with additional pesto and grated Parmesan.
Avoid slicing the loaves before they’re fully cooled. This particular cooling technique actually allows the bread to continue cooking even after the loaves are out of the oven.
You may also roll out the quartered dough before baking and spread the pesto on each quarter, then roll and bake, as typically done with cinnamon rolls.