For the dough:
1/4 cup sugar
1 tablespoon dry yeast
1 teaspoon ground cinnamon
1 teaspoon ground ginger
1/2 teaspoon kosher salt
1/8 teaspoon allspice
3 1/2 cups flour, divided
1 cup whole milk
2 tablespoons butter, room temperature
1 large egg
2 tablespoons molasses
For the filling and assembly:
1/2 cup packed light brown sugar
6 tablespoons butter, room temperature
1 tablespoon ground cinnamon
2 teaspoons ground ginger
1/4 teaspoon allspice
flour for the work surface
For the topping:
4 oz cream cheese, room temperature
1/2 teaspoon pure vanilla extract
1 1/3 cups confectioners sugar, divided
2 teaspoons molasses
1 teaspoon warm water
Mix the sugar, yeast, cinnamon, ginger, salt, allspice, and 1 ¾ cups of the flour together in a bowl until well combined. Heat the milk and butter until it reaches 105°F - 110°F.
Add the milk and butter mixture, eggs, and molasses to the dry ingredients in the bowl of a stand mixer and knead with the dough hook. Start at a low speed to incorporate everything together, then add the remaining 1 ¾ cups of flour gradually until the dough becomes smooth and pliable, about 5 minutes.
Move the dough to a buttered or oiled bowl, cover with a kitchen towel or plastic wrap, and let rise until doubled, about an hour.
While the dough is rising, start on the filling. Mix the brown sugar, butter, cinnamon, ginger, and allspice in a bowl until well combined. Prepare the baking dish and set it aside.
Once the dough has doubled, roll out the dough to a 12x16 inch rectangle on a floured surface. Spread the filling mixture, leaving a small margin of dough at the edges. Starting from the long edge of the dough, roll into a log. Slice the dough into rounds and place into the prepared baking dish cut sides up. Cover and let rise again until doubled in size, about an hour.
Preheat the oven to 375°F, bake the rolls for 20-25 minutes until golden brown. While the rolls are cooling, prepare the toppings. In one bowl, mix the cream cheese, vanilla, and one cup of confectioner's sugar until smooth. In a separate bowl, mix the remaining ⅓ cup confectioner's sugar, water, and molasses until smooth. Once the rolls have cooled to the touch, spread the cream cheese topping, then drizzle the molasses icing over top.