Using a stand mixer with a dough hook attachment, combine all dough ingredients (flour, milk, sugar, salt, vanilla bean paste, eggs, and butter) and mix on a low speed until the dough comes together as a smooth cohesive mass (5-10 minutes).
The dough should be slightly sticky. If it's too dry and won't come together, add an additional tablespoon or two of milk. If the dough is too sticky, add in an additional tablespoon or two of flour.
Transfer the dough to a lightly greased bowl, cover, and let rise in a warm place for 2 hours.
Filling
While the dough is rising prepare the filling.
In a medium bowl, combine the softened butter, brown sugar, and cinnamon. Mix together until it forms a thick paste. Set aside.
Place the dough on a lightly floured work surface and roll into a large 26x8 inch rectangle (you can also divide the dough in half and roll into two 14x8 inch rectangles if that's easier). Try to make the edges as even as possible. If the dough keeps shrinking back as you roll it out, cover and let it rest for 5-10 minutes to help the gluten relax before rolling again.
Spread the cinnamon sugar filling in an even layer over the top of dough, leaving about an inch of space at the top of the long end (this helps to seal the log).
Beginning at the long end, roll up tightly and pinch to seal. If desired, trim about 1 inch off of each end so that the log is 24 inches long.
For even slices, measure the dough and score the top at even intervals (about 1 inch apart).
Then using a very sharp serrated knife, or unflavored dental floss, cut the log into 24 1-inch pieces. [To cut with dental floss, break off a long piece and carefully slide underneath the dough. Then pull the ends of the floss and cross over the top. Pull gently to slice cleanly through the dough.]
Arrange the mini cinnamon rolls on the greased baking sheet.
Same Day Option: Cover loosely and let rise at room temperature for about 1 hour or until the dough has puffed up and filled in some of the empty space.
Overnight Option: Cover the pan tightly with plastic wrap and place in the refrigerator to rise overnight (8-16 hours). The next morning, remove from the fridge at let sit at room temperature while the oven is preheating.
Preheat the oven to 350°F.
Bake the mini cinnamon rolls for 20-30 minutes or until they are golden brown and cooked through. The filling will be bubbly.
Remove from the oven and let cool slightly while you make the glaze.
Spread the cheese frosting over the warm bite-sized cinnamon rolls and enjoy!
Notes
The mini cinnamon rolls and icing will keep in the fridge for up to 5 days.I recommend only icing a few cinnamon rolls at a time and storing the icing separately. Reheat your cinnamon roll in the microwave for about 30 seconds and then top with icing and will taste like it just came out of the oven!