Preheat the oven to 350°F (180°C). Line a 9-inch baking dish with parchment paper. Slightly oil the paper with cooking oil spray. Set aside.
In a large mixing bowl add the self-rising flour, vanilla yogurt, and melted plant-based butter. If your yogurt is unsweetened, you can add ¼ cup of sugar to sweeten the dough.
Stir with a rubber spatula, and when it starts to look crumbly, lightly oil your hands and knead to form a dough ball. If it is too wet, add a bit more flour. If too dry, add a bit more yogurt. You can also prepare this cinnamon roll dough in a stand mixer using the dough hook attachment. Work at speed speed 3-4 until a dough ball forms.
Lightly flour a work surface and place the dough on it. Sprinkle extra flour on top of the dough and roll into a 12.5-inch x 10.5-inch rectangle shape.
Spread the softened butter evenly onto the rectangle.
In a small bowl, whisk cinnamon and coconut sugar. Sprinkle the mixture and press it evenly onto the buttered dough.
Roll from the long side to form a cylinder.
Use a serrated knife or an unflavored dental floss string to cut 9 pieces from the cylinder.
Place each roll with the swirl facing up on the prepared baking dish.
Bake the rolls for 25-30 minutes at 350°F (180°C) until golden brown on top.
Cool down at room temperature on a wire rack before icing.
To glaze, stir ½ cup of powdered sugar with 1-2 tablespoons of almond milk and drizzle on top of the rolls.
