Preheat oven to 350°F / 175°C.
In a small saucepan, melt butter on medium heat, whisking constantly. It will foam up once or twice, but do not stop whisking. The second you see a light golden color in the center of the pot, remove from heat, continue whisking for another 30 seconds, and transfer to a large mixing bowl.
Add brown sugar, regular sugar, and salt to the butter, mixing thoroughly with an electric mixer on medium-low speed.
Crack an egg into the sugar and pour vanilla extract on the egg. Continue mixing on medium-low speed.
Add flour slowly, a quarter cup at a time on low speed. Do not overmix. Sprinkle in your mix-in of choice (chocolate chunks are our favorite, or chunks, peanut butter chips, and M&Ms!!) and fold them in with your hands, gently squeezing the dough.
Spread parchment paper onto two cookie sheets. For regular-sized cookies, form 1" balls or cubes of dough, placed 2" apart. This will yield 24 regular cookies, 12 on each pan. For large cookies, form 1½" balls or cubes of dough, placed 3" apart. This will yield 12 large cookies, 6 on each pan.
Place the first pan for 11-13 minutes. For regular cookies, cool them in the pan, sprinkle with salt, and serve.For large cookies, place a towel on the counter and drop the pan on its bottom 5 times on the towel, causing the puffy cookies to collapse and flatten. Return to the oven and bake an additional 3-4 minutes. Repeat dropping the pan 5 more times. Sprinkle with flakey salt and cool slightly before serving.