Pour milk into a microwave-safe bowl and heat in the microwave until warm but not hot to the touch, 45 to 60 seconds. It should be about 105 degrees F (41 degrees C). Pour into the bowl of a standing mixer.

Add 1 tablespoon sugar and yeast to the warm milk. Stir and let sit (proof) until foamy, about 5 minutes. Add 1/2 cup sugar, melted butter, eggs, and vanilla extract; stir with a dough hook until combined.

Add 4 cups flour, sea salt, and cinnamon; stir with the dough hook, starting on low speed and gradually increasing to high speed, until a large ball of smooth and slightly tacky dough is formed. Add 1 tablespoon flour at a time if dough seems too sticky, until a smooth ball is formed.

Transfer dough to a floured surface and knead with your hands until smooth and elastic, 3 to 5 minutes. Form into a ball and place inside a greased bowl. Cover the bowl with a warm, damp towel and let dough rise in a warm place until doubled in size, about 1 hour.

While the dough is rising, combine brown sugar, softened butter, and cinnamon for the filling in a small bowl until uniform throughout. Set aside.

Gently press the gas out of the dough and transfer to a large, floured work surface. Roll the dough into a 24x12-inch rectangle, about 1/4-inch thick. Spread the filling over the dough with greased hands or a greased spatula. Roll up the dough and cut into 12 equally sized rolls, about 2-inches long.

Line a 9x13-inch glass baking dish with lightly greased parchment paper. Place cinnamon rolls in the prepared baking dish in 4 rows of 3, evenly spaced. Cover and let rise until nearly doubled, about 30 minutes.

Meanwhile, preheat the oven to 350 degrees F (175 degrees C).

Bake rolls in the preheated oven until golden brown, 18 to 20 minutes.

While the rolls are baking, beat together powdered sugar, cream cheese, softened butter, vanilla extract, and salt for frosting. Keep at room temperature while rolls bake.

Spread frosting on warm rolls. Let cool before serving.