Begin the recipe by making the dough. In a small bowl stir together the 2 teaspoons instant yeast with the 5 tablespoons warm milk and a pinch of granulated sugar. Place the mixture aside in a warm spot for about 10 minutes, until it becomes foamy.
In a separate small bowl, whisk together the 1 cup all-purpose flour, 1 tablespoon granulated sugar, and ¼ teaspoon salt. Stir the yeast mixture into the flour mixture. Add in the 3 tablespoons melted butter. Stir until the mixture comes together to form a dough. Remove the dough from the bowl onto a lightly floured work surface. Knead with your hands for 5 minutes, adding an additional small amount of flour as needed. The dough will be soft but not overly sticky.
Form the dough into a ball and transfer it to a lightly oiled medium bowl. Cover with plastic wrap or a kitchen towel and store in a warm area to allow the dough to rise/double in size for about 30 minutes.
In a small bowl, stir together the 3 tablespoons brown sugar, 1 teaspoon ground cinnamon, with 2 tablespoons melted butter and set aside. Line a flat surface with parchment paper and lightly sprinkle with flour. Using a rolling pin, roll the dough out into a rectangle about 5×10-inches. Evenly spread the mixture on top of the dough.
Start at the shortest end of the dough and tightly roll to meet the other short end. Lightly oil a small baking dish and place the rolls into the pan. Allow them to rise for an additional 20 minutes or until they have doubled in size.
Place in the oven to bake at 400 degrees F. for 12 to 14 minutes. Allow the cinnamon rolls to cool in the pan while making the icing.
Make the icing for the cinnamon rolls by whisking together the ¾ cup powdered sugar, 2 ½ teaspoons milk, and ¼ teaspoon vanilla extract in a small bowl until creamy and smooth. Top the cinnamon rolls with the icing and serve immediately.
Store any leftovers in an airtight container at room temperature up to 3 days.