Heat oven to 350℉/177℃.
Spray an 8-inch square pan with baking spray. Set aside.
In a small bowl, combine cake flour, baking powder, and salt. Set aside.
With an electric mixer, beat aquafaba until stiff peaks form.
Add sugar 1 Tablespoon at a time, beating continuously. Set aside.
Heat coconut milk and coconut oil until heated through and melted.
Fold flour mixture into aquafaba mixture.
Gently stir in coconut milk mixture in 3 parts.
Fold in vanilla.
Pour into prepared pan.
Bake for 25-30 minutes, or until cake tests done.