In the bowl of a stand mixer fitted with a dough hook, combine the yeast, water, and sugar, and mix for 1 or 2 turns. Let stand for 3 to 4 minutes, until it foams.
Add 2 cups of the flour and mix at low speed to combine. Scrape down the side and bottom of the mixer bowl, and add the honey, oil, 3 of the eggs (see Kitchen Tips), the egg yolks, and the salt and mix to combine. Add the remaining 3 cups flour and mix at low to medium-low speed until incorporated.
Increase the speed to medium-high and knead the dough for 4 to 6 minutes, or until the mixture forms a discernable ball around the dough hook and is smooth and supple. This is a sticky dough that will not clear the side of the mixer bowl.
Place the dough in a bowl and cover with a damp kitchen towel or sheet of plastic wrap. Let it rise in a warm spot in the kitchen for about 80 to 90 minutes, until almost, but not quite, doubled in volume (see Kitchen Tips).
When the dough has risen, liberally dust a work surface with flour. Scoop the dough out onto it and knead for 30 seconds (see Kitchen Tips). Add more flour as necessary to prevent sticking. Knead for 1 minute. Divide the dough in half, pat both halves into a rough 5- by 7-inch shape, and cover one with plastic wrap and set it aside.
Line 2 rimmed baking sheets with parchment paper or Silpats. Flour a rolling pin. Place it the uncovered portion of the dough onto the work surface and gently dust it with flour. Roll it into an 8- by 12- to 14-inch rectangle, positioning the longer sides directly in front of you, parallel to the long sides of the kitchen counter. Be sure the dough isn’t sticking to the work surface as you roll it, by gently moving the whole thing around a bit on the work surface. If it sticks, sprinkle some flour under the dough, right where it is sticking. If the dough resists rolling and bounces back considerably with each roll, cover lightly with plastic wrap and allow to rest for 4 to 5 minutes.
Spread half the fig paste over the dough, leaving a 1-inch border around the perimeter uncovered. Scatter half the figs evenly over the filling, and sprinkle evenly with half of the graham cracker crumbs, and half the cinnamon, cardamom, and salt. Lift the exposed 1-inch edge that is closest to you and gently roll it up and over the filling, jellyroll style, rolling it up about 2 inches with each roll. Place the rolled, filled dough on one of the prepared baking sheets, with one end positioned right in the center. Coil the dough into a tight spiral. Neatly tuck the other end under the loaf.
Cover lightly with plastic wrap, and let rest for 15 to 25 minutes. Preheat the oven to 350°F. Repeat the rolling, filling and twisting with the second portion of dough while the first loaf rises.
Make an egg wash: Beat the remaining egg and the 2 tablespoons water in a small bowl. With a pastry brush, brush the risen loaf liberally with the egg wash, making sure to cover the sides and between the seams, and leaving enough egg wash for the second loaf. Sprinkle with half the cinnamon and turbinado sugar, if using.
Bake the first loaf for about 35 minutes, until the crust is a warm brown color, and the bread makes a hollow sound when rapped on the bottom. If you have an instant-read thermometer, insert it into the center of the bottom of the loaf; it will be done when the temperature reads 180° to 185°F (see Kitchen Tips). Transfer the loaf to a cooling rack and let cool for 30 to 40 minutes before cutting.
When the second filled, rolled loaf has rested, brush with egg wash and sprinkle with the remaining cinnamon and turbinado sugar, if using. Bake for 35 minutes, as directed above.