In a saucepan, melt the butter over medium heat. Continue to cook the butter for about 4-5 minutes, swirling occasionally to see the bottom of the pan, until the butter is very fragrant, and nutty, golden brown solids have formed on the bottom of the pan. Pour the brown butter, scraping up all of the browned bits, too, into a medium-sized mixing bowl, and let cool at room temperature for 30 minutes.
After cooling the brown butter, add the granulated sugar, brown sugar, egg, and vanilla, and whisk until smooth and lightened in color.
Separately, combine the flour, oats, salt, baking soda and cinnamon. Add the dry ingredients to the butter mixture, and stir together into a dough. Stir in the raisins.
Divide the dough into 12 portions (slightly less than what would fill a cupcake scoop), roll into balls, and flatten the balls slightly with the palm of your hand.
Line a large baking sheet with parchment paper, and place the dough balls 3 inches apart on the baking sheet. Place the pan in the refrigerator to chill for 20 minutes.
While the dough is chilling, preheat the oven to 350 F, and position a rack in the center of the oven.
Bake the chilled cookies on the center oven rack for about 8 - 8 1/2 minutes. They should appear set around the edges, but underdone in the middle. Do not over bake, or they will end up dry; they will set up to the perfect soft and chewy consistency as they cool.
Cool the cookies for 5 minutes on the baking sheet, then transfer to a cooling rack to cool completely.