Cardamom Orange Blossom Sourdough Braid

1. In a large bowl, mix the bread flour, whole wheat flour, salt, and ground cardamom together. 2. In a separate bowl, combine the sourdough starter, water, sugar, orange blossom water, and orange zest, then mix until well combined. 3. Pour the wet mixture into the dry ingredients and mix with your hands or a spatula until a shaggy dough forms. 4. Add the softened butter to the dough and knead on a floured surface for about 10 minutes, or until the dough is smooth and elastic. 5. Place the dough in a lightly greased bowl and cover with a damp cloth. Let it rise at room temperature for about 4-6 hours or until it has doubled in size. 6. Once risen, punch down the dough and let it rest for 30 minutes. 7. Divide the dough into three equal portions and roll each portion out into long ropes, about 16 inches in length. 8. Braid the three ropes together, pinching the ends to seal. 9. Place the braided dough onto a parchment-lined baking sheet and cover with a cloth. Let it rise for another 2 hours. 10. Preheat the oven to 375°F (190°C). 11. Beat the egg and brush it over the braided dough, then sprinkle sesame seeds on top. 12. Bake in the preheated oven for 25-30 minutes, or until golden brown and sounds hollow when tapped on the bottom. 13. Allow to cool on a wire rack before slicing.