Combine softened coconut butter and agave syrup until smooth, about 2 minutes. Gradually add oat flour, matcha powder, baking powder, and salt, mixing until a slightly sticky dough forms.

Chill the dough for about 30 minutes if sticky. Roll out on a floured surface to 1/4 inch thick, cut with cookie cutters, and place on a parchment-lined baking sheet.

Preheat oven to 350°F (175°C) and bake cookies for about 10 minutes, until edges are set and centers are slightly soft.

Cool cookies on the baking sheet for 5 minutes before transferring to a wire rack to cool completely for about 15 minutes.

Prepare optional frosting by mixing matcha powder with yogurt or melted coconut butter for a drizzle or glaze after cookies have cooled.