In a saucepan, melt the butter over medium heat. Continue to cook the butter, swirling the pan occasionally. When the butter starts to foam, and nutty golden brown solids have formed at the bottom of the pan, the butter is done. Scrape the browned butter, including all the browned bits, into a mixing bowl. Let cool at room temperature for 30 minutes.
Add the granulated sugar, brown sugar and molasses to the butter, and mix until well combined - you can use either a stand mixer, hand-held mixer or mix the dough by hand.
Beat in the eggs and vanilla until the mixture is smooth and ribbony.
Separately, combine the flour, oats, salt, baking soda and spices. Add the dry ingredients to the wet and mix until all the dry bits are incorporated.
Divide the dough into 20 portions (use a scant ice cream scoop/cupcake scoop to measure the portions). Shape each portion into a ball. Chill the dough balls in the refrigerator for 20 minutes.
Preheat the oven to 350 F, and position the oven rack in the center of the oven. Line a large baking sheet with parchment paper.
Place the chilled dough balls 3 inches apart on the baking sheet, and bake for exactly 8 minutes. The cookies will be just set around the edges, with a light golden color, and a gooey center. They will continue to cook and set up after you take them out of the oven, so DO NOT OVER-BAKE, or you'll end up with dry, crumbly cookies.
As soon as you take the cookies out of the oven, use a round cookie cutter (one that's larger than the circumference of the cookies), and "scoot" it around the hot cookie to pull in the edges - this will give you a perfectly round cookie.
Cool the cookies for 2 minutes on the baking sheet, then carefully transfer to a cooling rack. Cool completely before filling with the buttercream.