Heat oven to 350ºF. Line two baking sheets with parchment or silicon baking mats.
Add the walnuts to a food processor or blender; process until very finely ground, 20-30 seconds. Drizzle in the oil and process until a paste forms.
In a mixing bowl, beat together the walnut butter and butter until smooth. Add the sugar and maple syrup; beat until fluffy. Mix in the egg and vanilla.
Sift together the flour, baking powder, baking soda, and salt. Stir into the walnut mixture until completely incorporated.
Scoop teaspoons of dough onto the prepared baking sheets, leaving at least 2 inches in between each cookie. Bake 9-12 minutes, or until the edges are golden and the cookies are slightly puffy. Remove from the oven and gently press the centers down with a spatula. Let cool completely.