Make sure all ingredients are at room temperature. Pour milk into a small saucepan and add cubed butter. Heat it up very gently and slowly until milk is warm and butter is almost melted (it doesn't have to be melted completely but well softened). Set aside.
Prepare your dried ingredients by adding flour, salt, sugar and yeast into the bowl of your food processor (if you are using one) or just a regular bowl. Mix it slowly using a dough hook on your food processor or by hand until all the ingredients are combined. Add warmed milk and butter into your dry ingredients and keep mixing slowly while adding eggs.
Let your food processor knead the dough on a medium speed for good 10-15 min until it becomes soft and elastic. If you are kneading by hand I would allow good 15 minutes kneading time. It is normal for the dough to be slightly sticky but towards the end of kneading it should become easy to work with. If it's not add a bit more flour but be careful not to add too much.
Let the dough prove in a bowl covered with tea towel or clingfilm until it doubles in size (approx. 1-1.5hrs). Prepare your filling by washing and gently drying blueberries and mixing them up with icing sugar and cornflour. Be very gentle when mixing them as you don't want them to burst.
Once the dough finished proving, give it a quick punch to deflate it and turn it out onto the counter. Divide it into 4 roughly equal parts and then each of them into 4 roughly equal in size pieces. Don't worry too much if they are not exactly the same size (mine never are!).
Flatten all pieces of dough and divide prepared blueberry mixture in between all of them. Seal each one of the buns really well as if you were sealing a dumpling (sort of a crescent shape) and shape them gently in your hands to form a roll. Place seam side down on prepared baking tray. Repeat with all the other rolls. Once filled, let the rolls prove again on baking trays for approx 20-30 min (covered with clean tea towel). They should puff up a bit but won't double in size.
Bake in the oven preheated to 180C/350F/gas mark 4 for approx 15 min until nicely browned. You might have to bake them in batches due to the number of buns. Once baked take them out onto the cooling rack and let them cool completely before icing.
Prepare the lemon glaze by mixing icing sugar with lemon juice to reach desired consistency and brush or spoon gently over cooled buns. Best eaten on the day when baked but will still be tasty the following day.