Add the butter to a heavy bottomed skillet or saucepan. Melt butter over medium heat. Stir occasionally. You’ll start to see more and more bubbles as the butter cooks.After around 5 minutes, the butter will start to sputter and bubble. You’ll want to whisk it constantly now.

The butter will start to foam and you’ll notice little bits (milk solids) at the bottom of the pan. When you start to seem foam, the browning process will happen pretty quickly so do not stop stirring. 

When the butter becomes an amber color and you see small brown flecks in the foam, remove the pan from heat. Pour 1/2 cup of the butter into a bowl to use for the dough. Leave at room temperature.

Place the rest of the butter in a heat safe bowl or glass measuring cup. Place it in the refrigerator to cool to room temperature.**

In the bowl of an electric mixer, whisk to combine 3 1/2 cups flour, the sugars, yeast, and salt. Set aside.

Pour milk in a microwave safe bowl. Microwave in two 30 second bursts or until milk is warm to the touch (between 105 and 110 degrees Fahrenheit). 

Add the milk, eggs, vanilla extract and the brown butter to the flour mixture.

Use the dough hook and turn the mixer on medium. Mix for about 5 minutes or until dough first pulls away from the sides then wraps around the hook. Dough should be tacky but shouldn't stick to dry hands. If, after 5 minutes, dough is still sticky, mix in another 1/4 cup of flour. Mix. Touch again with a dry hand. If dough is still sticky, add two tablespoons at a time until dough is no longer sticky. Dough should be tacky but should not stick to dry hands. 

Place dough into a large mixing bowl coated with oil. Cover bowl with a clean kitchen towel. Set bowl in a warm, draft free place for about an hour, or until dough has doubled in size. 

While dough is rising, prepare the filling. In a medium sized bowl, combine the brown sugar, cinnamon and salt. Set aside.

Once dough has doubled, punch dough down. Turn dough out onto a lightly floured surface. Shape/roll dough out into a 12 x 16 inch rectangle. Use an offset spatula, the back of a spoon or your hands to spread the chilled spreadable (but not melted) brown butter*** over the rectangle but leaving a 1/4 inch border along the edge furthest away from you. Sprinkle all of the filling evenly over the butter. Use your hands to rub the cinnamon sugar mixture into the butter. 

Start at the longest side of the rectangle (and the edge that's closest to you). Roll the dough into a log, moving your hands from side to side as you roll it all the way up. Keep the roll tight (but not too tight). Once the log has formed, flip it seem side down. Seal or pinch the edge of the dough as best as you can. Push the ends of the dough in towards each other if the log became too long while rolling it. You can also shape it a little if it's a little thicker on one side. Use a sharp knife to cut off about 1 inch from each end. Set those pieces aside. 

Use a sharp knife or a long string of unflavored dental floss to slice the log in half. Slice each half in half then slice each section into three one-inch pieces.  

Place the rolls into a 9 x 13 inch rectangle lined with parchment paper and sprayed with baking spray. Cover the pan with a clean kitchen towel and set aside to rise for about 30-45 minutes. Preheat oven to 350 while the rolls are rising. 

Remove kitchen towel. Bake for 23-28 minutes or until rolls are slightly golden brown. 

In a large bowl or the bowl of a stand mixer fitted with the paddle attachment, mix the cream cheese and butter on medium speed for one minute until creamed and combined. Add the brown sugar and mix on medium for another minute. Mix in the vanilla then turn the mixer on low and gradually mix in the powdered sugar.