Mix the dry ingredients. Combine the flour, yeast and salt the the bowl of an electric mixer fitted with a dough hook.
Warm the wet ingredients. In a small saucepan, combine the butter, milk and brown sugar. Heat over low until the butter has melted. Remove from heat and make sure the temperature of the liquid is between 110˚F - 120˚F. If needed, let the mixture cool.
Knead the dough. Stir the warm liquid into the flour mixture, followed by the eggs and mix at a low speed. Once the dough comes together, increase the speed to medium and continue to knead the dough until it is smooth an elastic - about 5 minutes.
Proof the dough. Transfer the dough into a greased mixing bowl and cover with plastic wrap or a clean dish towel. Allow the dough to rise in a warm space until it has doubled in size - about 30-40 minutes.
Make the filling. Melt the remaining dairy free butter in the microwave (about 30 seconds). Then, mix the cinnamon, brown sugar and melted butter in a mixing bowl until evenly combined.
Shape the rolls. Working on a floured surface, roll the dough to a rectangle approximately # x # inches. Spread the filling in an even layer over the dough and roll lengthwise to form a long roll. Use dental floss or a serrated knife to gently cut the dough into 12 individual rolls.
Second proof. Grease a large baking dish (9x13"). Transfer to your prepared baking dish and cover again. Allow the rolls to rise a second time for about 20-30 minutes or until the rolls has filled in the pan.
Bake the cinnamon rolls. While the rolls rise, preheat your oven to 350˚F. Bake the cinnamon rolls for 20 - 25 minutes, or until the rolls are golden brown on top and the center is fully cooked - if you're not sure, the internal temperature should reach about 190˚F for doneness. Remove the cinnamon rolls from the oven and allow them to cool for about 5 - 10 minutes before frosting.
Make the glaze. Add the dairy free cream cheese to a large mixing bowl. Microwave for about 30 seconds to soften/melt the cream cheese. Stir until smooth. Then, whisk in the dairy free milk and vanilla extract. Then, whisk the powdered sugar into the mixture, one cup at a time, until you reach your desired consistency. The glaze should be thick but still pourable.
Frost the cinnamon rolls. While the rolls are still warm, pour the glaze over the cinnamon rolls and spread the glaze as needed with a rubber spatula.