Step 1

Preheat oven to 350 degrees and butter a 9x13 inch baking pan. (see note)

Step 2

In a large bowl (or the bowl of a stand mixer) stir together 2 cups flour, yeast, sugar, and salt.

Step 3

In a glass/liquid measuring cup combine milk and butter and microwave on high for 30 seconds at a time, stirring after each, until butter is mostly melted and milk is very warm. (see note) Add milk mixture and egg to the dry ingredients and mix well.

Step 4

Mix in remaining flour, 1/2 cup at a time, until a shaggy dough forms.

Step 5

Knead for 5 minutes, then transfer to a lightly greased bowl and cover tightly with plastic wrap. Let rise for 10 minutes.

Step 6

Roll dough into a large rectangle (about 15x12 inches) and rub softened butter all over the top of the dough.

Step 7

Stir together sugar, brown sugar, and cinnamon. Sprinkle over butter, leaving about 1/2 inch around the edges bare.

Step 8

Tightly (but gently) roll the dough from one long side toward the other. Pinch the seam to seal off the length of the dough.

Step 9

Use a sharp knife or unflavored dental floss to cut into 12 equal-size pieces. Place each cut-side down in your prepared baking pan.

Step 10

Cover tightly and let rise in a warm dry place for 30 minutes.

Step 11

Uncover, bake on center rack for 30-35 minutes until golden brown on the top. Allow to cool slightly before frosting.

Step 12

In a medium sauce pan melt butter over medium-high heat. Once melted, continue to stir for 2-3 minutes longer until color changes from pale yellow to deep golden. Remove from heat.

Step 13

In a large bowl cream together the browned butter, cream cheese, and vanilla.

Step 14

Alternate mixing in 1 cup of powdered sugar and 1 tablespoon of milk until icing is smooth and fluffy. Mix in a pinch of salt for added richness, then spread over cinnamon rolls.

Step 15

Serve immediately or cover tightly and store at room temperature up to three days. Reheat individual rolls in the microwave for 20-30 seconds.