Preheat oven to 180°C/350°F (160°C fan). Lightly grease then line three baking trays with paper.
Brown butter - Melt butter in a small silver pan or saucepan over medium heat. Leave to simmer on medium heat for 3 to 5 minutes, stirring every now and then, until you see little golden-brown bits. Immediately pour the butter and all the brown bits into a large mixing bowl and set aside to cool for 5 minutes.
Chop choc - Cut the chocolate into 1cm /¼" pieces. Transfer the chunks into a bowl and leave the fine chocolate dust behind for another purpose.
Mix dry ingredients - Whisk flour, oats, baking soda, and salt in a large bowl.
Back to the butter - Add sugar to the brown butter and whisk. Add egg and vanilla, whisk until smooth.
Finish dough - Add dry ingredients into the egg-butter mixture. Mix with a wooden spoon until the flour is almost mixed in. Add chocolate, and stir until mixed through and you can no longer see flour. Set aside for 5 minutes to let the mixture firm up a bit.
Cookies - Scoop a heaped tablespoon of dough onto the tray, 5 cm / 2" apart. Flatten to 8 mm / ⅓" thick, reshaping sides if needed.
Bake - Bake 2 trays for 11 minutes, switching shelves and rotating the tray at the 7 minute mark, or until the surface is light golden. For 1 tray, bake 10 minutes, rotating the tray at the 6 minute mark.
Cool on the tray for 10 minutes, then transfer onto a cooling rack to fully cool.
