Place butter in a small saucepan over medium heat. Let sit on heat until butter has melted and browned slightly, releasing a nutty aroma. Transfer to a heat and freezer safe container and let cool slightly, then place in freezer for 30-45 minutes.
Remove butter from freezer and let soften ever so slightly (you just want it to be able to mix well with the sugar.) I microwaved it for about 30 seconds to help it soften up.
Preheat oven to 350 degrees Fahrenheit. Line two cookie sheets with parchment paper and set aside.
In a medium mixing bowl, combine flour, oats, baking powder, baking soda, cinnamon and salt. Set aside.
In the bowl of a stand mixer, combine brown butter and brown sugar. Mix at medium speed until the two ingredients are well incorporated, then mix in the eggs and vanilla. Add the dry ingredient mixture and beat until just combined. Remove bowl from stand and stir in apples and butterscotch chips using a wooden spoon or spatula.
Using a small cookie scoop (or a tablespoon measure,) scoop dough onto prepared cookie sheets, leaving only about an inch and a half of space in between each scoop. Flatten dough slightly with hands before baking.
Bake in 350 degree oven for 10-12 minutes, or until cookies are a light golden brown. Remove from oven and let cool on cookie sheet about 5 minutes, then transfer to a cooling rack.
While cookies are cooling, make the bourbon glaze. Combine powdered sugar, almond milk (or regular milk) and bourbon (or more milk if making this recipe for kids) and mix using a stand mixer, hand mixer or whisk until a glaze has formed. Scoop glaze into a piping back or gallon-size resealable plastic bag. Cut off the tip of the bag and drizzle glaze generously over the cookies. Let dry about 15 minutes before serving.
These cookies can be stored in an airtight container for up to a week.