In a microwave-safe container, mix the milk, water, and 1/3 cup of browned butter. Warm it up for 30 to 45 seconds; ensure it’s just warm, not hot.

In a big bowl, combine the instant yeast, salt, flour, and granulated sugar. Whisk everything together until well mixed.

Stir in 2 more cups of flour, mixing until a dough starts forming. Gradually add in 1 to 1 1/2 cups more flour until the dough is shaggy and slightly tacky. Knead it until you have a smooth ball, adding flour bit by bit if it’s too sticky.

Cover the dough with a cloth or plastic wrap and let it sit for 10 minutes to relax the gluten.

On a lightly floured surface, roll out the dough into a rectangle measuring 12 by 16 inches. Spread the cinnamon filling evenly on top, leaving a border of 1/2 inch.

Carefully roll the dough from the long edge into a log. Use unflavored dental floss to cut the ends off, then slice into 12 equal pieces.

Place the rolls in a parchment-lined 9 by 13 inch baking dish. Cover them and let proof in a warm spot for about 45 minutes, or in a switched-off preheated oven, until they double in size.

Remove the rolls from the proofing oven, if they were in one. Preheat your oven to 350°F and bake for 25 to 30 minutes, until the tops are a light golden brown.

Check that the solidified brown butter is softened but not melted. Mix the brown butter with cream cheese until it’s smooth. Then, stir in powdered sugar, vanilla, milk, and a pinch of salt until creamy.

Once the rolls are warm, spread the icing over the tops so it melts in. Enjoy them right away!