In a large glass bowl or stand mixer, add flour, sugar and salt together. Give it a quick mix.
Add the softened butter. Mix it in using your finger tips until mixture resembles bread crumbs.
In a separate jar or bowl, add lukewarm milk and instant yeast together. Mix and add it to the flour mixture. Add the eggs and mix using a spatula or wooden spoon until mostly combined (by hand) or fully combined (stand mixer).
Tip the dough onto a clean working surface and knead until the dough comes together (a stand mixer would've already done most of the kneading for you). The dough will be quite sticky but resist adding any additional flour. Shape into a bowl and place in a clean glass bowl. For the first rise, cover with plastic wrap or a clean cloth and place in the warmest area in your kitchen for 1 hour 30 minutes or until doubled in size. Note: I like setting the oven to around 35°C/95℉ with any type of heat setting. Let the appliance heat up for 5 minutes and then switch off the oven. Then put the bowl with the yeast dough in the oven cavity.
Meanwhile, prepare the filling, frosting and baking dish. Note: I add a layer of cream to the base of the oven proof baking dish. This helps the base of the cinnamon rolls become caramelized and gooey. You can add less or more cream, depending on your preference.
Once the dough has risen, lightly oil a clean surface and tip the dough onto the surface. Using a rolling pin, roll the dough into a rectangular shape about 35cm x 28cm x 8cm. Spread the brown butter-cinnamon sugar filling.
Using a very sharp, non-serrated knife, cut the dough into 9 strips. Roll each one up and place in an oven proof dish on top of the cream (if using). You should have 3 rows of 3. For the second rise, cover with a dry clean cloth and allow to rise for 30 - 45 minutes. Meanwhile, preheat the oven.
Bake at 190℃/375℉ for 20-30 minutes. This will depend on how brown and crispy you'd like the rolls to be. Allow to cool for 15 minutes before pouring over the frosting.