Warm 1/4 cup of the milk to 110°F and pour it into a medium bowl, then stir in 1 teaspoon of the granulated sugar and sprinkle the yeast over the top; let sit for 5 to 10 minutes until foamy.
In a large bowl or stand mixer bowl, combine the remaining 3/8 cup granulated sugar, beaten eggs, salt, melted butter, and remaining 3/4 cup warm milk, then add the foamy yeast mixture and stir to combine.
Add the flour gradually, mixing with a dough hook or wooden spoon until a soft, slightly sticky dough forms, then knead for 8 to 10 minutes until smooth and elastic.
Place the dough in a lightly greased bowl, turn to coat, cover, and let rise in a warm place for 60 to 75 minutes, or until doubled in size.
Lightly flour your work surface, punch down the risen dough, and roll it into a large rectangle about 12 by 16 inches.
Spread the apple butter evenly over the dough, leaving a 1/2 inch border along one long edge.
In a small bowl, stir together the brown sugar, 1/4 cup granulated sugar, and 1 tablespoon cinnamon, then sprinkle the mixture evenly over the apple butter.
Starting from the long side opposite the bare edge, roll the dough up tightly into a log and pinch the seam to seal.
Cut the log into 12 equal slices and arrange them cut side up in a greased 9 by 13 inch baking pan with a little space between each roll.
Cover the pan and let the rolls rise in a warm place for 30 to 40 minutes, or until puffy and touching.
Preheat the oven to 350°F while the rolls finish rising.
Bake the rolls for 18 to 22 minutes, or until lightly golden on top and the centers look set.
While the rolls bake, beat the cream cheese, powdered sugar, maple syrup, 1/2 teaspoon cinnamon, and pinch of salt in a medium bowl until smooth and fluffy.
Remove the rolls from the oven and, while still hot, spread the maple cream cheese frosting evenly over the tops so it melts into the swirls.
Let the frosted rolls cool for 10 to 15 minutes, then serve warm.