In a small bowl, stir together the water, yeast, and sugar. Set aside for 5 minutes, or until the yeast is foamy.
Make the dough: In a medium bowl, combine the coconut oil, almond milk, sugar, and salt. Stir in the yeast mixture. Place the flour in a large bowl, then add the wet ingredients and stir until combined. The mixture will be sticky. Use your hands to roughly knead the mixture, then turn it out onto a floured surface. Knead the dough for 3 to 4 minutes, or until smooth, sprinkling it with more flour if needed. Form the dough into a ball.
Brush a large bowl with coconut oil and place the dough inside. Cover with plastic wrap and set aside in a warm place to rise until doubled in size, about 1 hour.
Make the filling: In a small bowl, mix the brown sugar and cinnamon.
Punch down dough and roll out on a floured surface into a 20x14-inch rectangle. Brush with 2 tablespoons melted coconut oil and sprinkle with the cinnamon sugar to within ½ inch of the edges.
Starting at one of the short 14-inch ends, roll tightly into a log, then use a sharp knife to slice the log into 12 rolls. Place the rolls in the baking dish cut-side up, cover, and let rise for 1 hour.
Preheat the oven to 350°F.
Make the glaze: In a medium bowl, whisk together the powdered sugar, 3 tablespoons almond milk, and vanilla until smooth. If it’s too thick, add more almond milk.
Uncover the rolls and bake for 25 to 30 minutes, or until lightly golden on top. Remove and allow to cool for 10 minutes, then drizzle the glaze on top and serve.