In a small bowl combine warm milk and yeast. Let sit for 5–10 minutes until foamy.
Add melted butter, egg, sugar, and salt, then mix until combined.
Gradually add flour, mixing until a soft dough forms.
Transfer the dough to a floured surface and knead for 6–8 minutes until smooth and elastic.
Place the dough in a greased bowl, cover, and allow it to rise for 1 hour or until doubled in size.
Roll the dough into a rectangle about ¼ inch thick.
Spread softened butter evenly over the dough.
Mix brown sugar and cinnamon, then sprinkle it over the dough.
Add rainbow sprinkles evenly across the filling.
Roll the dough tightly into a log and cut into 12 equal rolls.
Place the rolls in a greased baking dish and let them rise again for 30 minutes.
Preheat the oven to 350°F (175°C) and bake for 20–25 minutes until golden.
In a bowl whisk powdered sugar, milk, vanilla extract, and green food coloring until smooth.
Drizzle the green icing over the warm cinnamon rolls and sprinkle extra rainbow sprinkles on top if desired.