Preheat oven to 350°F (180°C) and line a baking sheet with parchment paper.
In a large bowl, combine the rolled oats, flour, baking powder, and sugar. If using walnuts or dried fruit, add them now.
Melt the butter, then whisk in the eggs and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and mix thoroughly until a uniform dough forms.
Drop spoonfuls of dough onto the prepared baking sheet, and flatten them slightly into cookie shapes.
Bake the cookies for 12-15 minutes, or until golden brown. Let them cool on the baking sheet for a few minutes, then transfer to a wire rack to cool completely.
Before serving, dust with powdered sugar or serve with fresh fruit, if desired.
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