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Prepare the dough: Combine 1 cup flour with the water, sugar, eggs, yeast and half-and-half in the bowl of a stand mixer fitted with a paddle attachment. Stir on low speed until combined. Let stand, undisturbed, 2 minutes, then gradually stir in 2 cups flour on low speed.
Switch to the dough hook attachment, set the machine to medium speed, and add as much of the remaining flour as necessary (an additional 2 to 3 cups) to make a dough that just cleans the side of the work bowl. Gradually add the butter and salt, then continue beating on medium speed until the butter is no longer visible, 1 to 2 minutes, scraping down the sides of the bowl and the dough hook as necessary. Cover the finished dough with a clean towel, transfer it to a warm location and let it rest, allowing the dough to double in size, 1 to 2 hours. (You can also cover the dough with plastic wrap and refrigerate overnight. Let the dough come to room temperature for 30 minutes before continuing.)
While the dough rises, make the date paste: Add the dates, lemon juice and 1 cup/235 milliliters water to a small saucepan. Cook over medium-low, stirring occasionally, until the dates are completely softened and the texture of applesauce, 6 to 8 minutes. Stir in the orange zest, cinnamon and cardamom. Transfer to a shallow bowl to cool.
After dough has risen, remove the dish towel, punch the dough down and turn it out onto a floured work surface. Butter 2 9-inch cake pans. Using floured hands or a floured rolling pin, press or roll the dough flat and into a rectangular 15-by-10-inch shape. Use a spoon to spread the date mixture evenly over the dough, then roll the dough crosswise into a tight, 15-inch-long cylinder. Cut into 14 rolls (each a little wider than 1 inch) and transfer the rolls to the prepared cake pans, arranging 7 rolls in each pan so spirals are visible. Cover loosely with plastic wrap and let the dough rise a second time, 20 to 30 minutes.
While the rolls are rising, heat oven to 350 degrees. Once the rolls have risen, bake until deeply golden-brown, 30 to 35 minutes.
As rolls bake, make the caramel sauce: Add the sugar, corn syrup and 1/4 cup/60 milliliters water to a medium saucepan. Cook over medium-high, undisturbed, until the sugar turns a light amber color, about 10 minutes. Remove saucepan from heat and whisk in the butter until melted and incorporated, then whisk in the cream and sea salt. When the buns are done, drizzle the caramel sauce on top, saving a little sauce to brush on any remaining dry spots. Serve the buns warm.