In the bowl of a stand mixer fitted with a dough hook stir together Water (1/2 cup), Brown Sugar (1/3 cup) and Active Dry Yeast (2 teaspoon). Allow to proof for 7-8 minutes.
Stir in Raisins (1 cup), Vegetable Oil (1/4 cup), Large Egg (2) and yolks of the other Large Egg (2) to the proofed mixture.
To this mixture add 2 cups of the All-Purpose Flour (2 1/4 cup), Salt (1 teaspoon), Ground Cinnamon (1 tablespoon), and Ground Cardamom (1/8 teaspoon). Begin kneading, allowing all the flour to be absorbed.
Add remaining 1/2 cup of Flour gradually until dough begins to pull away from the sides and is smooth, about 7-8 minutes. The dough will be a little sticky but you should be able to handle it without additional flour.
Lightly oil a large bowl and turn out dough into bowl flipping to coat sides. Cover loosely with a clean kitchen towel and allow to rise in a draft-free area for 90 minutes. (It will not appear to be double in size).
Remove dough and knead a few times to punch out the air. Divide dough into 3 equal portions of approximately 300g each. Allow dough to rest for about 5 minutes. This helps relax the dough and will make it easier to roll into logs.
Line a large baking tray with parchment.
Roll each third into a 14-inch long log. Lay the 3 logs parallel to each other on the baking tray.
Braid dough tightly, pinching the ends together and tucking under slightly.
Cover loaf with a clean kitchen towel and allow to rise in a draft free area for 45 minutes.
Before the dough is done rising, preheat oven to 350 degrees F (175 degrees C).
In a small bowl whisk together the final whole Large Egg (1) and Cream (1 tablespoon). Brush generously on the loaf and sprinkle with Coarse Sugar (to taste).
Bake for approximately 32 minutes until golden and an internal temperature of 195 degrees F (90 degrees C) is reached.
Remove from oven and transfer to cooling rack. Allow to cool prior to slicing.