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In the mixer, dissolve the yeast in the warm water and milk. Add the sugar and salt, mix and let sit for a couple minutes.
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Add half of the flour while mixing on low, then add the melted butter.
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Add the rest of the flour (or until the dough pulls away from the bowl).
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Add the egg and mix for about 5 minutes.
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Either cover the mixer and let the dough rise to double in there OR dump the dough in a bowl and cover it. I like to have my oven warm (heated to 170 then turned off) and a pan of boiled water in the bottom. I put the bowl in the oven and have the warmth and humidity help it rise quicker. Otherwise, let it sit on the counter until it rises double in size.
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Either way, once it's doubled, separate the dough into two equal parts.
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Roll out each part into a rectangle.
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Brush melted butter all over each one and sprinkle with lots of brown sugar and some cinnamon. Using the longest side, roll up the dough.
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Use string or dental floss to cut into rolls (about an inch wide).
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Place rolls, separated on a greased cookie sheet.
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Cover and let rise again, until about doubled in size.
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Bake at 350 for 9-11 minutes, or until you see a hint of golden brown on top.
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In the meantime, make your glaze by heating up the glaze ingredients in a saucepan.
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Drizzle over cinnamon rolls.