To make the starter roux—also called water roux or tangzhong, add 3/4 cup of whole milk into a small pot over medium heat, stirring constantly.
Add the 1/4 cup of cake flour when the milk is warm and continue to whisk—keep whisking until you see thick, slow bubbles appear.
Remove the pot from heat and allow the mixture to cool; it will continue to thicken as it cools down; it should have the consistency of a loose paste.
When the mixture has cooled to room temperature, transfer it to the mixing bowl of a stand mixer fitted with a dough hook.
Add the light brown sugar, yeast, one egg, kosher salt, heavy cream (1 1/2 cups), and remaining cake flour (6 1/2 cups of cake flour).
Mix for 17 to 25 minutes, scraping down the sides as necessary. When the dough passes the windowpane test, it's ready.
The windowpane test is done by pinching off a nice piece of dough (about the size of a ping-pong ball) and flattening it on a clean cutting board or countertop.
Then, hold the flattened dough between your fingers and slowly stretch it out; if it stretches without breaking and allows you to see light passing through it, it's ready.
If not, knead it a few minutes more and try again.
Now, adjust the mixer speed to medium and begin adding the cubed pieces of room-temperature butter a little at a time until it is fully incorporated.
Mix for about 5-8 minutes or until the dough pulls cleanly away from the sides.
Remove the dough hook and place the mixing bowl on the countertop.
Next, drape a warm, damp kitchen towel over the mixing bowl and place the dough in a warm place until it has doubled in size; this may take up to 45 minutes to up to an hour and a half.
Punch the dough down and scatter a handful of all-purpose flour onto a clean surface. Roughly work the dough with your hands or a rolling pin into a large rectangle with the narrow end facing you.
Melt the remaining 1/2 stick of butter and brush the dough, leaving 1-inch of space around the edge of the dough.
Add the blueberry compote, use more of the blueberries, and brush on some of the compote syrup; you don't want to make the dough soggy.
Now, scatter on a cup of light brown sugar.
Start at the narrow edge of the dough away from you, and begin rolling the dough towards you.
Don't roll the dough too tightly because the cinnamon rolls may not rise properly if it's too tight. Using a very sharp knife, serrated bread knife, or non-flavored dental floss, cut the roll into 1" to 1 1/2" rolls.
Place the rolls cut-side down into a cake pan with parchment paper on the bottom and brushed with melted butter on top of the parchment paper and along the walls of the 9-inch pan or skillet.
Cover the rolls with a damp kitchen towel and allow them to double in size; this process can take up to 45 minutes, depending on conditions.
Bake in a 350-degree oven for 20 - 25 minutes until golden brown.
Remove the Blueberry Cinnamon Rolls from the oven and allow them to cool.
Glaze generously with Cream Cheese Lemon Icing.
Serve.