Preheat your oven to 350°F (175°C) and line a large baking sheet with parchment paper.
In a large mixing bowl, stir together the four tablespoons of warm melted butter, two tablespoons of oil, and 1/2 cup of coconut sugar until smooth.
Whisk in the room temperature large egg and pure vanilla extract for one full minute until the mixture looks glossy and completely cohesive.
Add the all-purpose flour, quick-cooking oats, baking soda, ground cinnamon, and fine table salt directly into the bowl over the wet base.
Switch to a sturdy spoon or spatula and fold gently just until the flour disappears and a thick, sticky cookie dough forms.
Use a standard 1 tablespoon measuring spoon to drop the dough onto your prepared baking sheet, leaving about two inches of space between each cookie.
Bake at 350°F (175°C) for ten to twelve minutes until the edges are beautifully golden brown but the centers still look slightly soft.
Remove from the oven and let the cookies cool completely on the baking sheet until they are 100% cold.
In a small, wide bowl, whisk together the powdered sugar and tablespoon of milk until it forms a very thick, smooth glaze.
Take a completely cooled cookie and gently press just the bumpy top surface directly down into the thick icing, then lift straight up.
Place the cookie back onto the parchment paper to let the icing catch only on the high ridges of the oats, creating a shattered ice look.
Let the iced cookies set undisturbed for ten minutes until the glaze completely hardens before serving.