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Make the cupcake batter:
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1. Preheat the oven to 350 degrees Fahrenheit. Lightly butter or line 12 muffin cups with paper liners.
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2. In the bowl of an electric mixer, or with a hand mixer, whisk together the flour, mochiko, sugar, baking powder, and salt. Add 1/2 cup of the butter, eggs, egg yolks, yogurt, lemon zest, and vanilla extract. Beat everything together at medium speed until the batter is smooth and satiny, about 30 seconds. Scrape down the sides of the bowl.
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3. Evenly fill the muffin cups with the batter and bake for about 20 to 25 minutes or until pale gold and a toothpick inserted into a cupcake comes out clean. Remove from the oven and place on a wire rack to cool.
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Make the buttercream:
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4. Place the remaining 1/2 cup of butter in a large mixing bowl. Add 2 cups of the powdered sugar and the lemon juice. Using an electric mixer, beat until smooth and creamy on medium speed, about 3 to 5 minutes.
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5. Gradually add the remaining sugar, 1 cup at a time, beating well after each addition (about 2 minutes), until the icing is thick enough to be of good spreading consistency.
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6. Add the chopped basil and stir in until evenly incorporated. Use and store the frosting at room temperature because the frosting will set if chilled. The frosting can be stored in an airtight container for up to 3 days.
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Assemble the cupcakes:
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7. Once the cupcakes have completely cooled, use a paring knife to cut a small well in the center of each cupcake top. Pipe the lemon curd into the center of each cupcake, then frost the top of the cupcake with the buttercream frosting. These cupcakes are best the day they are made, although they will keep for a few days at room temperature.
