Start by activating the yeast in warm milk. Heat 1 cup of soy milk over medium heat until the milk is warm but not too hot to touch (about 100 degrees F). Stir in the yeast and set aside for 10 minutes to allow the yeast to activate. The yeast will start to bloom (grow) when it’s ready.
To make the dough, begin by making the chickpea egg. Combine the remaining ¼ cup milk with chickpea flour, whisking it together until thick and gooey. Set aside.
In the large bowl of a stand up mixer, combine 2 cups flour, sugar, salt, and vegan butter. Using the hook attachment, mix to combine. With the motor running, slowly add the chickpea flour and yeast/milk mixture, scraping down the sides as necessary. Add the remaining flour ½ cup at a time and beat to combine. Add flour until the dough starts pulling away from the sides of the bowl. It should be soft and pillowy to the touch. Alternatively, you can do this in a large bowl with a wooden spoon.
Transfer to a floured surface and kneed the dough for about five minutes. Shape into a ball and place in a large oiled bowl. Cover the dough in plastic wrap, and place in a warm area of your house for 1 hour or until the dough has doubled in size.
When the dough is ready, roll out onto a floured covered surface into a large rectangle about ¼ ” thick. Spread the vegan butter over the entire surface of the dough, leaving the top ¼" of the rectangle clean. Combine cinnamon and sugar and spread evenly over the butter. Starting at the bottom of the rectangle, roll dough evenly into a tight roll. With your fingers press together the seam. Seam side down, cut dough using a serrated knife into 15 equal pieces, about 1” thick. Place cinnamon rolls in an oiled 9x12 (or similarly sized) pan. Cover and allow the dough to rise for a second time until doubled in size, about 40 minutes.
Preheat the oven to 350 degrees F. Once cinnamon rolls are ready, remove plastic wrap and brush tops and sides with soy milk. Bake for 25–30 minutes, until golden brown and fragrant. To check for doneness, lightly tap the tops of the rolls. They should sound hollow when tapped.
Remove the rolls from the oven and transfer them to a cooling rack, allowing them to cool for 10 minutes. While the cinnamon rolls cool, combine ingredients for the glaze and, once they are ready, pour the glaze over the top.