Warm a dry skillet over medium heat and toast the oats, stirring often, until just fragrant and lightly golden, 3–4 minutes. Transfer to a plate to cool completely.
Heat the oven to 350°F (177°C). Line 2 baking sheets with parchment paper.
In a medium bowl, whisk together the flour, baking soda, fine salt, and cinnamon; set aside.
In a large mixing bowl, beat the softened butter and brown sugar on medium-high until light and fluffy, about 2 minutes, scraping the bowl once.
Add the peanut butter and granulated sugar and mix on medium until smooth and creamy, about 1 minute. Beat in the egg and vanilla just until cohesive, 20–30 seconds.
Stir the cooled toasted oats into the wet mixture with a spatula. Add the dry ingredients in two additions, mixing on low only until the last streaks of flour disappear. Let the dough rest for 10 minutes to hydrate the oats for extra chew.
Scoop 1½-tablespoon portions (about 30 g) onto the prepared sheets, spacing 2 inches apart. Lightly press the tops to a thick disc and sprinkle with a tiny pinch of flaky sea salt if using.
Bake 10–12 minutes, rotating the pans halfway, until the edges are set and the centers look slightly soft. Tap each sheet once on the counter right after baking to settle the cookies. Cool on the pan for 7 minutes, then transfer to a rack to finish cooling.
Store in an airtight container at room temperature for up to 4 days, or freeze baked cookies (or dough balls) for up to 2 months.