In a medium bowl, add flour, 3 tbs granulated sugar, and salt, stirring together to combine.
In another bowl, whisk together milk, oil/ butter, and eggs until combined. Add wet ingredients and cheese into the dry ingredients, using a spatula to stir together until just combined. (Lumps in the pancake mixture are good because it means you haven’t over-mixed.)
Cover, and place batter in the refrigerator to rest for 30 minutes.
Meanwhile, in another medium bowl, mix blueberries, 1 tbs granulated sugar, and (optional) rosemary to combine.
Reserve until needed. When pancake batter has rested, in a large nonstick pan, melt 1 tbs butter over medium-high heat.
Portion 1/4 cup amounts of batter onto pan, slightly flattening pancake with the back of a spatula.
When bubbles form on the edges of the pancake’s surface, flip pancake with a spatula.
Cook until that side is browned, just another 1 to 2 minutes.
Transfer to a paper towel-lined plate.
Continue with remaining batter, adding 1 tbs butter for each batch, until batter has resulted in about 12 pancakes.
Serve sprinkled with confectioners’ sugar and reserved blueberries.