In a large bowl or bowl of a stand mixer fitted with a dough hook, combine the non-dairy milk, yeast, and granulated sugar. Allow mixture to sit for about 5 minutes, to allow to yeast to activate. After the 5 minutes have passed, stir in the maple syrup, salt, and flours. The mixture may seem too sticky, but at this point start kneading the dough in the bowl to get all the flour into the dough. You can also use your mixer with the dough hook to knead the dough as well. Knead for a minute, just working the dough enough to make it pliable. If the dough seems really sticky at this point, add a couple tablespoons of flour to make it easy to handle.
Cover the bowl with a towel and allow to rise in a warm spot for at least an hour.
While the dough is rising, prepare the filling by combining all the ingredients in a small bowl and set aside.
Grease a round cake pan and set aside.
After the dough has risen, lightly flour a flat surface and roll the dough out into a rectangle that is 14-inches by 12-inches. The measurement doesn’t have to be exact, just as long as it’s around that shape.
Spread the filling mixture onto the rolled out dough, spreading to just shy of the edges.
Roll the dough up lengthwise (starting with the long edge) into a big log. Slice into 1 1/2-inch pieces and place cut side up (like a cinnamon roll) into the pan.
Cover with a towel and allow to rise again for an hour. Preheat oven to 375°F while rolls are rising.
Bake for 20 minutes, or until golden brown.
Allow the rolls to cool for 10 minutes. While the rolls are cooling, whisk together the frosting ingredients until smooth.
Pour the frosting over the rolls and serve immediately.