Preheat oven to 350 degrees and line baking sheets with parchment paper.
In the bowl of an electric mixer or in a large bowl with a hand mixer, beat butter, granulated sugar, and brown sugar until light and fluffy, about 3 minutes.
Mix in egg and applesauce until well-combined. Add the oats, flour, baking soda, baking powder, cinnamon, salt, and both raisins and mix until just combined.
Using a 1 ½-inch cookie or ice cream scoop, drop dough onto prepared baking sheets about 2 inches apart.
Bake cookie for 13-15 minutes, until the edges start to brown. Allow the cookies to cool on the baking sheet for about 5 minutes then transfer them to a wire rack to finish cooling.
When cookies are completely cooled, drizzle glaze over them.