Whisk flour, yeast, sugar, and salt together in a stand mixer bowl. Combine warm milk, eggs, vanilla, and softened butter; add to dry ingredients. Mix on low with dough hook for 2 minutes until combined, then knead on medium for 8 to 10 minutes until smooth and slightly tacky.
Transfer to an oiled bowl, cover, and let rise in a warm spot for 60 to 90 minutes until doubled in volume. A finger pressed 2cm into the dough should leave an indention that fills slowly.
Mix softened butter, brown sugar, cinnamon, and nutmeg into a thick spreadable paste for the filling.
Turn risen dough onto a lightly floured surface and roll into a 45x35cm (18x14-inch) rectangle, 6mm thick. Spread cinnamon filling evenly to the edges, leaving a 1.5cm border on the far long edge.
Roll the dough tightly from the near long edge toward the far edge. Pinch the seam firmly. Cut into 12 equal rolls using a serrated knife or dental floss. Arrange cut-side up in a greased 9x13-inch baking dish with small gaps between each roll.
Cover and let rolls proof for 30 to 45 minutes until visibly puffed and touching. Preheat oven to 190°C (375°F).
Bake 22 to 26 minutes until tops are deep golden-brown and the center roll reads 88°C (190°F) internally. Cool in the dish for 10 minutes before frosting.
Beat softened cream cheese and butter until smooth. Add sifted powdered sugar in two additions, then vanilla and salt. Add milk to reach a thick, flowing consistency. Spread generously over the warm rolls.
