Preheat the oven to 350 degrees Fahrenheit. Microwave the whole milk until it reaches 110 degrees Fahrenheit on a thermometer. Add active dry yeast and 1 teaspoon of sugar. Let sit for six minutes while yeast gets frothy.
Add room temperature eggs, canola oil, and ½ cup of sugar into the yeast mixture and stir well. Pour into the bowl of a stand mixer with the dough hook attachment. Add gluten free flour, kosher salt, cream of tartar and baking soda to the bowl and beat on medium speed for 2 minutes, scraping the bowl after 15 seconds to incorporate all the flour. The dough should be sticky.
Using a spatula scrape the dough out of the bowl and into a large greased bowl. Brush the top of the dough with oil and cover with saran wrap. Set aside and let rise for two hours.
Meanwhile sprinkle flour over a large work surface. Once the dough has risen place it onto the floured area and sprinkle flour onto the dough. Roll it out into a rectangle about 11 by 13 inches long. Using an offset spatula spread the butter mixture evenly on the dough leaving a ¼ in gap on all sides.
Starting with the long side (closest to you) roll the dough up into a log shape. Cut into 9 rolls similar in size (doesn't have to be exact).
Nestle the rolls into a greased 8 by 8 pan in rows of three. Let the rolls rise for 45 more minutes and then bake on the middle rack for 30 to 34 minutes until the tops are golden brown and the insides are soft but baked. Make the icing.