Brown the butter in a saucepan over medium heat, stirring, until amber and nutty, about 5 to 7 minutes. Pour into a heatproof bowl and cool to room temperature, roughly 20 minutes.

Beat the cooled browned butter with both sugars until grainy and lighter, about 2 minutes. Add the egg, yolk, and vanilla, beating 1 minute until smooth and glossy.

Whisk the flour, baking soda, salt, and cinnamon together. Stir into the butter mixture until just combined, then fold in the oats.

Scoop dough into 2-tablespoon mounds, place on a tray, cover, and refrigerate at least 30 minutes. Heat oven to 350°F (175°C). Place chilled mounds 2 inches apart on parchment-lined baking sheets.

Bake 10 to 12 minutes until edges are golden and centers look slightly underdone. Cool on the pan for 5 minutes, then move to a rack and serve warm or at room temperature.