Pour milk, 1 tablespoon of the sugar, and yeast into a standing mixer fitted with a dough hook. Allow to sit for 5 minutes. The mixture should foam, signaling that the yeast is active.
Add in the remaining sugar along with the vanilla bean paste, eggs, and 1 cup of the flour. Turn mixer to low and allow to come together. Once mixture is combined, add in remaining flour and knead for about 10 minutes. Dough is ready when it pulls away from the sides of the bowl, has a smooth surface, and be stretchy to the touch. Note that it is a wetter dough, so this is OK!
Coat a large bowl with oil and place the dough into the bowl. Cover with plastic wrap and set in a warm area to proof for 1 hour.
In a small bowl, combine the brown sugar and cinnamon for the filling. Lightly grease a 9"x 13" baking pan. Set both aside.
Liberally four a large work surface. Roll the dough out into an 16"x 24" rectangle. It will be thin, but this is what you want! Spread the melted butter over the dough, coating it evenly. Sprinkle on the brown sugar/cinnamon mixture and rub into the butter to combine.
Working from the long edge, roll the dough into a log, pinching the ends so it stays together. Using a serrated knife or dental floss(even better!), cut the dough into 12 equal buns. Place into prepared pan.
Allow dough to rise a second time. Cover the pan with a cloth and let rest in a warm place for 1 hour.
Preheat the oven to 375°F. Bake for 20-30 minutes, until the cinnamon buns are golden brown on top.
While the buns are baking, make the vanilla bean cream cheese frosting. In a medium bowl, whisk together all ingredients, mixing until fully combined. Mixture will be thick, but you're about to microwave it to thin it out.
Once the buns are out of the oven, cool for 10 minutes. Microwave the frosting for 10-15 seconds to thin it out slightly, then spread over warm cinnamon buns and serve!