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In a medium bowl, place 2 tablespoons (19g) of the dry Soft Golden Roll & Bun Mix; set it aside to use in the filling (step 4).
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To make the dough: In a large bowl or the bowl of a stand mixer fitted with the dough hook, stir together the remaining mix, yeast, and brown sugar. Add the butter and milk and stir to form a soft, shaggy dough. (This should take about 30 seconds by hand or about 1 minute with the mixer; some dry patches are OK at this point.)
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If working by hand, transfer the dough to a greased surface and use greased hands to knead the dough until smooth, about 5 minutes, using a bowl scraper to release any sticky dough from the surface as needed. If using a mixer, knead the dough on medium-low speed for 3 to 5 minutes, until smooth. Return to the bowl, cover, and let rest for 5 minutes.
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To make the filling: To the medium bowl with the reserved mix, add the brown sugar and cinnamon, stirring to combine. Add the melted butter, stirring until the mixture looks like damp sand.
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To assemble the cinnamon rolls: Lightly grease a metal 9" x 13" pan (If baking with glass, see "tips," below.). Transfer the dough to a greased work surface and press it into an 8" square. Use a rolling pin to roll the dough into a 16" x 14" rectangle.
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Sprinkle the filling evenly over the dough, covering all but a 1/2" strip along one long side.
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Starting with the filling-covered long side, roll the dough into a log. Pinch the seam to seal, if necessary.
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Score the dough lightly into 12 equal pieces, about 1 1/4" to 1 1/2" wide. Cut the dough at the score marks using dental floss for the cleanest slices. (Pull off a long piece of floss, loop it underneath the log at the score mark, and pull the ends in opposite directions to cut the dough. Repeat until you've cut all of the cinnamon rolls.) If you don’t have dental floss, use a bench knife or sharp knife to slice the log.
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Place the cinnamon rolls into the prepared baking pan in a 4 x 3 pattern. Cover with lightly greased plastic wrap or a reusable cover and let the rolls rise for about 45 minutes; about 20 minutes into the rise, preheat the oven to 350°F with a rack in the center. The cinnamon rolls are ready to bake when they look puffy and an indent remains when they’re pressed gently with a floured fingertip.
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Bake for 20 to 25 minutes, until the centers bounce back when gently pressed. (They won’t brown much.) A digital thermometer inserted into one of the center rolls should read 190°F.
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Remove the cinnamon rolls from the oven and place the pan on a rack to cool for 10 to 15 minutes before icing.
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To make the icing: In a large bowl, whisk together the confectioners’ sugar, melted butter, 2 tablespoons (28g) of the milk, and vanilla. Add more milk as needed to create a thick but pourable icing.
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Spread the icing over the cinnamon rolls and serve immediately. If you’re planning to serve the cinnamon rolls later, wait to ice them until just before serving. Store icing at room temperature, tightly covered, until you’re ready to use it.
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Storage information: These cinnamon rolls are best eaten the day they are made. Store any leftover rolls well-wrapped at room temperature for up to 2 days. Warm leftover rolls for 10 to 20 seconds in the microwave or wrap in foil and heat in a preheated 350°F oven until warmed through, about 5 to 8 minutes.
