Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a medium bowl, whisk together the rolled oats, all-purpose flour, baking soda, ground cinnamon, and salt.
In a large bowl, use an electric mixer to cream the softened unsalted butter, granulated sugar, and brown sugar until light and fluffy, about 2-3 minutes.
Add the unsweetened applesauce and vanilla extract to the butter and sugar mixture. Mix until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined.
Fold in the raisins evenly into the cookie dough.
Using a tablespoon or cookie scoop, drop rounded spoonfuls of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, or until the edges are golden brown but the centers remain soft.
Remove the cookies from the oven and allow them to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.