Heat the milk in a small saucepan until just simmering.
Add the milk to a large mixing bowl, then add the butter and sugar. Whisk to combine, until the butter has melted.
Check the temperature of the milk mixture. If it's just warm to the touch or cooler, then it's fine to continue. If it feels hot, wait for it to cool down.
Once the milk mixture has cooled enough, whisk in the eggs. Add the starter and whisk to combine.
Add the flour and salt and use a wooden spoon or spatula to mix until a soft, shaggy dough forms. Cover and set aside to rest for 20 minutes.
Do three rounds of stretches and folds over the course of an hour, one round every 20 minutes. After this, the dough should be soft and relatively smooth.
Place the dough smooth-side up back into the mixing bowl. Cover with a tea towel or plate, and set aside in a warm, draft-free place to rise until doubled in size. Depending on ambient temperature and the strength of your starter, this can take anywhere from 4-10 hours.
Once the dough has risen, you have two options. One, refrigerate for at least 2 hours before continuing. Two, skip the chilling step and move right to step 10, rolling and shaping. We recommend chilling.
Place the risen dough into the refrigerator, in the mixing bowl (don't deflate the dough) and cover well. Chill for 2-12 hours.
After chilling, tip the dough out onto a lightly floured surface.
Shape and Fill
Grease a large baking dish with butter.
Pat the dough into a rough round. Roll it into a log, then turn it so that it's seam-side up, and the short edge is facing you. Roll it into a log again from this direction. See this post on shaping boules for a visual guide.
Roll the dough out into a large rectangle, about 30x40cm (12x16 in.) in size.
Brush the softened butter onto the rolled out dough - this is why chilling is so helpful - then top with the brown sugar and cinnamon in an even layer.
Roll the dough into a log again, working from the short end, and making sure it's rolled very tightly.
Cut the log into 10 equal pieces with unflavoured dental floss or a very sharp knife.
Place the rolls into the prepared baking dish, leaving a small space between each to allow for expansion during proving.
Cover the dish with a tea towel and set aside at room temperature to rise for another 1-2 hours, or until puffy but not doubled in size.
Baking and Storing
Preheat the oven to 350°F (180°C).
Place the baking dish onto the centre rack of your oven and bake for 20-25 minutes, or until golden in colour and the tops of the rolls feel firm to the touch.
Remove the dish from the oven and cool for at least 15 minutes before serving. Leftover cinnamon rolls will keep for up to 3 days at room temperature and freeze well in a sealed container, but are best fresh.
If topping with cream cheese frosting, do so immediately before serving. Frosted rolls will not store very well.