Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a mixing bowl, combine the all-purpose flour, rolled oats, granulated sugar, brown sugar, baking powder, and salt. Mix well.
In a separate bowl, cream the softened butter and vanilla extract together until light and fluffy.
Gradually add the dry ingredients to the butter mixture, mixing until just combined.
Gently fold in the raspberries, being careful not to mash them.
Using a tablespoon, drop dough onto the prepared baking sheet, spacing them about 2 inches apart.
If using, sprinkle crumble topping over each cookie.
Bake in the preheated oven for 10-12 minutes, or until the edges start to turn golden brown.
Remove from the oven and allow to cool on the baking sheet for 5 minutes before transferring to a cooling rack to cool completely.