Mix the dough: Place the sourdough starter, 1 egg, 2 egg yolks, honey, oil, and water in the bowl of a stand mixer fitted with the bread hook attachment. To the wet ingredients, add the all purpose flour, whole wheat flour, salt, and active dry yeast. Mix the dough on 2nd speed for 3 minutes and then increase to 4th speed for 5 minutes (if you have a mixer other than a Kitchen Aid, mix for 3 minutes on slow speed and 5 minutes on medium speed). The dough will come together and be relatively smooth but still quite slack and tacky.