Cook's Note: Quinoa flour can be found at health food stores.
For the cupcakes: Place an oven rack in the center of the oven. Preheat the oven to 350 degrees F. Line a 12-cup muffin pan with paper liners. Set aside.
Whisk together the flours, baking powder and salt in a medium bowl.
Beat the sugar and butter in a large bowl until combined, using an electric hand mixer. Add the eggs, milk and vanilla. Beat until smooth. Add the dry ingredients and mix until just blended. Spoon half of the batter into the prepared muffin cups (about 2 tablespoons of batter in each cup). Spoon 1 teaspoon of the strawberry fruit spread into the center of the batter. Spoon the remaining batter on top to cover the fruit spread completely. Bake until puffed and the cake springs back when touched, 15 to 17 minutes. Transfer to a wire rack and cool completely, about 30 minutes.
For the frosting: Place the chocolate chips in a small bowl over a small pan of barely simmering water. Heat, stirring occasionally, until the chocolate is melted and smooth, about 2 minutes. Remove the pan from the heat.
Beat the butter in a medium bowl until light and smooth, using an electric hand mixer. Beat in 3 cups of the powdered sugar, milk and vanilla until smooth and creamy. Remove half of the frosting and place in a small bowl.
Add the melted chocolate to one bowl of the frosting and stir until smooth.
Stir the strawberry fruit spread and the remaining 3/4 cup powdered sugar into the other bowl of frosting and stir until smooth.
Frost the tops of the cupcakes with desired frosting using a small spatula. Allow the frosting to set for 20 minutes before serving.