Add the sourdough discard, light brown sugar, warm milk, melted butter, and egg to the bowl of a stand mixer with the paddle attachment. Mix on low speed until the ingredients are mixed thoroughly.
Switch the paddle attachment with the dough hook attachment. Then, add the flour, instant yeast and salt to the bowl. Mix on low, stopping to scrape the sides of the bowl with a rubber spatula when necessary, until all of the ingredients have been incorporated.
Continue to knead the dough for 5-7 more minutes at medium speed. You know the dough has been thoroughly kneaded when the dough is pulling away from the sides of the bowl while it is being kneaded and it feels tacky, not sticky, when you poke it.
Remove the dough and place it in a lightly greased straight-edge bowl, cover it and let the dough rest until doubled in size in a warm spot.
While the dough is rising, prepare your fillings. Combine the blueberries, sugar, lemon juice, lemon zest, cornstarch and salt in a medium skillet over medium heat. Smash the blueberries while stirring constantly with a wooden spoon or fork. Continue to cook the blueberry filling until thick and glossy, about 5-8 minutes.
In a separate bowl, combine the butter, sugar, lemon zest, vanilla extract and salt until smooth. Set aside.
Once the dough has doubled in size, remove the dough onto a lightly floured work surface. With a rolling pin, shape the dough into a 16 inch by 12 inch rectangle.
Spread the softened lemon butter over the entire surface of the sourdough sweet roll dough. Top the remaining blueberry compote on top of the lemon filling and spread over the entire dough in an even layer.
Using a pizza cutter, slice the dough into 12 even stripes (about 1 ⅓ inch each) then roll each into a roll for a more polished look.
Grease a 9 x 13 metal baking pan with butter before gently placing the Sourdough Discard Lemon Blueberry Sweet Rolls inside, about ½ - 1 inches apart.
Cover with plastic wrap and let rise for a second time until they have noticeably grown and look puffy.
Preheat the oven to 350 degrees F and bake the rolls for 24-28 minutes or until the tops are golden brown and the internal temperature is 190-200 degrees F.
Remove from the oven and place the sweet rolls on a wire rack to cool slightly.
While the sweet buns are cooling, prepare the lemon cream cheese frosting. In a large mixing bowl with a hand mixer, mix butter and cream cheese until combined. Add powdered sugar, blueberry compote, lemon juice, lemon zest and salt and blend until smooth.
Using an offset spatula, spread the lemon cream cheese frosting over the warm sweet rolls so that it can slightly melt into all of the cracks and crevices.
