Cream the Butter: Add the butter and brown sugar to a large mixing bowl or standing mixer. Cream over low speed for 2 to 3 minutes, scraping the sides of the bowl with a spatula, until the butter has lightened in color and the sugar is dissolved.
Wet Ingredients: Add the applesauce and vanilla and cream until incorporated, about 1 minute
Dry Ingredients: Add the flour, baking powder, cinnamon, and salt to the bowl. Mix over low speed until just incorporated, being careful not to over mix.
Add-Ins: Add the walnuts and oats to the cookie dough and fold in with a spatula. Then, add the blueberries to the bowl and carefully fold again, trying not to pop any of the berries.
Divide the Dough: Divide the dough into 12 thick cookies (about 1/3 cup of dough per cookie) and transfer to a lightly greased or lined baking sheet. Lightly flatten each cookie, as they will not spread in the oven during baking.
Chill: Place the cookies in the refrigerator for at least 15 minutes while you preheat the oven to 375. You can also make the cookies in advance, cover, and store in the refrigerator overnight.
Bake: Bake in the middle rack of the oven for 16 to 18 minutes, until the bottom edge of the cookies is lightly browned. Let the cookies rest on the baking tray for 5 minutes, then transfer to a wire rack to let cool completely.
Serve & Store: Enjoy immediately, or store in a container with a loose-fitting lid at room temperature for up to 2 days. Because of the high moisture content of the blueberries these cookies will spoil faster; to prevent this, you can also store in the fridge for up to 7 days (or the freezer for up to 2 months) and reheat in the toaster oven until warmed.