Position racks in upper and lower thirds of oven and preheat to 350°F. Line two baking sheets with parchment paper.

In a medium bowl, whisk together flour, oats, baking soda, cinnamon, and salt until evenly combined.

In a large bowl, beat butter with both sugars on medium speed until light and fluffy, about 3 minutes. Scrape down bowl and beat in eggs one at a time, then vanilla, until fully incorporated.

Reduce mixer to low and gradually add dry ingredients, mixing just until no flour streaks remain. Do not overmix.

Gently fold in white chocolate with a spatula. Add blueberries and fold carefully 2 to 3 times to distribute without crushing. The dough will look streaky with berry juice - this is fine.

Using a 2-tablespoon scoop or heaping tablespoon, drop dough 2 inches apart onto prepared sheets. Bake 10 to 12 minutes, rotating sheets halfway through, until edges are golden and centers look slightly underdone. Cool on sheets 5 minutes, then transfer to wire racks.