Transfer the oats, flour, baking soda, salt, and cinnamon to a mixing bowl and stir well until combined.

Whisk together the melted butter and sugar in a separate bowl. Mix in the egg and pure vanilla extract until the wet ingredients are well combined. Pour the wet ingredients into the bowl with the dry ingredients and mix until the dough is well combined.

Refrigerate the dough for at least 20 minutes (up to overnight).

Preheat the oven to 350 degrees Fahrenheit and line a large baking sheet with parchment paper.

Use a small cookie scoop or a spoon to scoop mounds of dough onto the lined baking sheet. Leave a couple of inches of space between each dough mound to allow space for the cookies to spread.

Bake on the center rack of the preheated oven for 11 minutes, or until the cookies are golden brown around the edges.

Allow the cookies to cool to room temperature on the cookie sheet.

Mix the powdered sugar and milk (or water) in a wide-mouth bowl until the glaze is nice and creamy. Dip the tops of each cookie into the glaze, and allow the glaze to drip off before moving them to a plate or a wire rack to dry completely.