Line slow cooker with a piece of parchment large enough to go up the sides.
Turn slow cooker to warm, and set aside.
To make the rolls, add milk, sugar, yeast, and water to the bowl of a stand mixer fitted with a paddle attachment.
¼ cup warm milk, ¼ cup granulated sugar, 1 tablespoon active dry yeast, ¾ cup warm water
Give it a stir, and then let it sit for 5-10 minutes, or until foamy.
Add in butter, and stir to combine.
¼ cup salted butter
Add 2 cups flour and salt.
½ teaspoon salt
Switch to dough hook, and knead in.
Continue adding flour in 1/4 cup increments until dough clings to paddle and clears the sides of the bowl. Dough should feel a little sticky but shouldn't stick to your finger if you poke it.
Place dough on a floured surface, and roll out to an 9x13-inch rectangle.
Spread softened butter over dough.
¼ cup salted butter
Combine sugars and cinnamon, and sprinkle over butter.
⅔ cup granulated sugar, ⅓ cup light brown sugar, 1-2 teaspoons ground cinnamon
Roll up lengthwise, and gently press together the seam.
Cut dough into 12-14 pieces, depending on desired size of cinnamon rolls.
Place slightly apart in 5-quart oval slow cooker.
Cover opening with a thin cotton towel, and let sit for 10 minutes.
Turn slow cooker to high, and cover with slow cooker lid.
Cook for approximately 1 ½ hours.
Remove from slow cooker, and prepare icing.
To make the icing, beat together cream cheese and butter until well-combined.
Continue beating, adding additional milk as necessary to get desired consistency.
Drizzle or spread icing over warm cinnamon rolls.
Notes
Milk: Using whole milk will give you richer, softer dough. However, you can use whatever milk you have on hand.
Yeast: You can substitute an equal amount of instant yeast for the active dry yeast.
Butter: If using unsalted butter, increase the salt in the dough to 3/4 teaspoon and add a pinch of salt to the filling and frosting.
Cream cheese: I recommend using full-fat cream cheese for the richest icing. You could also use 1/3-less fat cream cheese, but I don't recommend using fat-free cream cheese.
Foil collar: I've found that my slow cooker has hot spots. Chances are yours does, too. If it does, make yourself a foil collar in your slow cooker to ensure even "baking".