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