Combine all of the dough ingredients in the bowl of an electric mixer fitted with the dough hook. Mix on medium speed until it comes together in a cohesive ball, about 4 to 7 minutes. Transfer the dough to a lightly oiled bowl, turn to grease all sides, cover with plastic wrap, and let rise until doubled, about 1 hour.
Transfer the dough to a lightly floured work surface, and divide it into two even balls. Roll each portion of dough into a 8 x 20-inch rectangle. Spread each piece of dough with 3 Tablespoons of butter. Stir together the brown sugar and cinnamon and sprinkle evenly over the dough.
Starting with the short end, roll each rectangle of dough into a log. Using a serrated knife, cut each log into 20 1-inch slices. Gently place the slices in a greased mini muffin tin. Let the buns rise at room temperature until they’re nearly doubled, about 30 minutes. Preheat the oven to 400°F.
Bake the buns in a until they’re golden brown, about 15 minutes. While the buns are baking, beat together the cream cheese, butter, sugar, and vanilla. Spread the frosting on the top of the buns while ether are still warm from the oven. Serve immediately.