In a stand mixer, combine flour, yeast, brown sugar, salt, and ground ginger. Gradually add warm milk and butter, mixing until incorporated. Mix in eggs, molasses, and vanilla extract, slowly adding remaining flour until a soft dough forms.

Knead the dough on high speed for 4 to 5 minutes until smooth and elastic. Cover and let the dough rest in a warm place for about 20 minutes.

Prepare the filling by mixing brown sugar, ground cinnamon, ground ginger, butter, and molasses in a bowl until combined.

Roll the rested dough into a 12x16-inch rectangle and spread the filling evenly over it. Roll the dough into a tight log and pinch the seams.

Cut the log into 12 equal pieces and arrange in a greased baking dish. Cover and allow to rise for about 1 hour until doubled in size.

Preheat oven to 350°F. Bake the rolls for approximately 40 minutes until golden brown.

Prepare frosting by beating cream cheese and butter in a bowl until smooth, then mix in molasses, ground ginger, ground cinnamon, and powdered sugar.

Spread cream cheese frosting over warm rolls and enjoy!