In a food processor, whirl coconut until finely ground. Then add butter, brown sugar, vanilla, all-purpose flour, and masa flour and whirl together until smooth. Or, mince coconut with a knife. Then, in a bowl, with an electric mixer on medium speed, beat butter, brown sugar, and vanilla until smooth; stir in coconut, all-purpose flour and masa flour until mixture is no longer crumbly and starts to come together in a ball.
Press dough evenly into two 9-inch round pans with removable rims. Press edges of dough with fork tines to make a ridge pattern. Then, with fork tines, pierce dough all over in parallel lines 1 inch apart.
Bake shortbread in a 300° oven until firm to touch and slightly darker brown, about 45 minutes. In a small bowl, mix granulated sugar and cinnamon; sprinkle over hot shortbread. Let cool 10 minutes.
Remove pan rims from warm shortbread. Cut each round into 12 wedges. Cool completely on pan bottoms on racks.
Note: Nutritional analysis is per cookie.