Adjust the oven racks to the upper-and lower-middle positions and heat the oven to 375 degrees F. Line 2 large baking sheets with parchment paper or spray them with nonstick cooking spray.
In a medium bowl, whisk the flour, salt, baking powder and cinnamon; set aside.
In the bowl of a stand mixer with the flat beater attached, cream the butter and brown sugar at medium speed until light and fluffy, about 3 minutes. Scrape down the sides of the bowl with a rubber spatula as needed. Add the egg and vanilla; beat at medium speed until combined, about 30 seconds. Add the dry ingredients and beat at low-speed until just dough comes together, about 30 seconds. Add in milk. If dough is still crumbly, add milk 1 tablespoon at a time until it comes together. Fold in blueberries gently with a spatula.
Place the ½ cup sugar for rolling in a shallow bowl. Fill a medium bowl halfway with cold tap water. Dip your hands in the water and shake off any excess (this will prevent the dough from sticking to your hands and ensure that the sugar sticks to the dough). Roll a heaping tablespoon of dough into a 1½-inch ball between moistened palms, roll the ball in the sugar, and then place it on the prepared baking sheet. Repeat with the remaining dough, moistening your hands as necessary and spacing the balls about 2 inches apart (you should be able to fit 12 cookies on each sheet).
Bake until the cookies centers are just set and very lightly colored, 15 to 18 minutes, rotating the baking sheets front to back and top to bottom halfway through the baking time. Cool the cookies on the baking sheets about 3 minutes; using a wide metal spatula, transfer the cookies to a wire rack and cool to room temperature. Store in an airtight container at room temperature.