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To make the dough: In a large bowl or the bowl of a stand mixer fitted with the flat beater attachment, combine the water, butter, sugar, egg, yeast, and salt. Then, add the flour and mix until a smooth, sticky dough forms, about 1 minute on medium speed. If making by hand, there may be some lumps — that’s OK.
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Cover the dough and set aside for 20 minutes.
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On a lightly oiled or (gluten-free) floured work surface, gently knead the dough. This dough is more delicate than traditional wheat dough; knead it by folding it in half towards you, using a bowl scraper as needed, patting it down, rotating 90° (a quarter turn) and folding again — until it becomes firmer to the touch, smoother, and easier to handle, 5 to 6 times. As you work, dust your work surface and the dough lightly with gluten-free flour (or apply more grease), as needed, to prevent sticking. The dough should become noticeably less sticky.
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Cover and allow the dough to rise for 40 minutes, or until puffy.
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To make the filling: While your dough is rising, combine the filling ingredients in a small bowl until sandy and homogenous; set aside. Grease an 8" round cake pan.
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On a greased or floured surface, gently deflate your dough and knead 5 to 6 more times. Use additional gluten-free flour or grease on your hands and work surface as needed. By this time, the dough will be more pliable but still slightly sticky to the touch.
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To shape the rolls: Pat or roll the dough into a 10" x 12" rectangle about 1/2" thick.
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Sprinkle the filling evenly over the dough. Starting from the long side, roll up the dough to form a 12" log.
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Cut into eight 1 1/2" pieces and place into the prepared pan. Cover and allow the rolls to rise for 20 to 30 minutes, or until slightly puffy.
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While your rolls are rising, preheat the oven to 350°F.
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To bake the rolls: Bake the gluten-free cinnamon rolls for 30 to 35 minutes, or until the rolls are browned. Set the rolls aside to cool for 15 minutes or until just slightly warm to the touch.
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To make the glaze: While the cinnamon rolls cool, whisk together all of the glaze ingredients in a medium bowl until well combined.
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Spread the glaze evenly over the rolls. If you prefer more of a frosting texture that doesn’t sink into the rolls, apply the glaze when the rolls are fully cooled. Cool completely before serving or enjoy warm.
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Storage instructions: The gluten-free cinnamon rolls are best enjoyed the day they’re made but they can be stored airtight at room temperature for up to 2 days. Reheat in a low-temperature oven (300°F) or in the microwave in short increments.