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To make the dough: In the bowl of a stand mixer fitted with the dough hook, combine the milk and butter. Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Add it to the bowl along with all of the remaining dough ingredients, mix briefly to combine, and scrape down the sides of the bowl.
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Knead on low speed until a soft, sticky dough forms, about 5 minutes, stopping to scrape the bowl once midway through.
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Cover the bowl and let the dough rise at room temperature until doubled in volume, 1 to 1 1/2 hours.
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Preheat the oven to 350°F with the rack in the center. Lightly grease a 9" x 13" pan.
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To make the filling: While the dough is rising, combine the filling ingredients in a small bowl. Mix until a homogeneous, thick paste forms. Set aside.
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To assemble the gingerbread cinnamon rolls: Transfer the dough to a lightly floured work surface and roll it into a 10" x 15" rectangle. For evenly shaped rolls, pat the dough into a proper rectangle with squared-off corners, rather than an oval.
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Use an offset spatula to spread the filling evenly across the surface of the dough, covering all but a 1/2" strip along one long side.
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Starting with the filling-covered long side, tightly roll the dough into a 15" log. Pinch the seam closed along the length of the uncovered long edge.
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Score the dough lightly into 10 equal 1 1/2" pieces. Slice the dough into individual rolls at the score marks using dental floss or a serrated knife.
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Place the gingerbread cinnamon rolls into the prepared pan, cut-side up, spacing them evenly in staggered pairs. Cover the rolls and let them rise for 20 to 30 minutes, until they’re puffy and don’t bounce back immediately when gently pressed.
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Bake the gingerbread cinnamon rolls for 20 to 25 minutes, or until they are lightly golden brown on top and a digital thermometer inserted into the center of one roll reads 190°F. Allow the rolls to cool slightly for 10 to 15 minutes.
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To make the cream cheese icing: While the rolls are cooling, beat the cream cheese in a stand mixer fitted with the flat beater until smooth. Add the butter and mix the icing until completely homogenous, scraping down the sides of the bowl as needed. On low speed, gradually add the confectioners’ sugar and mix until fully incorporated and smooth.
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Spread the icing onto the warm rolls and serve warm or at room temperature.
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Storage information: Store leftover gingerbread cinnamon rolls in the refrigerator, covered, for up to 2 days. Reheat before serving.
