Preheat oven to 350°F. Line a 12-cup muffin tin with paper liners and set aside.
In a medium bowl, whisk together flour, baking powder, salt and baking soda. Set aside.
With an electric mixer, cream butter and sugar until fluffy, about 5 minutes. Beat in eggs one at a time, scraping down sides of bowl and mixing well between additions. Alternate adding flour mixture with Chobani in three additions, starting and ending with flour.
Divide the batter among the muffin cups, filling each about two-thirds full. Bake until golden and a cake tester inserted into center comes out clean, 15-20 minutes. Cool 10 minutes, then turn cupcakes onto wire rack to cool completely before frosting.
For the frosting, melt the chocolate in the microwave, stirring every 15 seconds until it is completely melted, 2-3 minutes. Set aside to cool, 15-20 minutes.
Use a fork to mash in the butter, stirring and scraping the bottom and sides of the bowl often, until the butter is incorporated. Add the Chobani and use a whisk to combine. Do not over-mix or the frosting will become grainy. If it turns grainy, whisk in the remaining butter a little at a time until the frosting is smooth.
Frost the 12 cupcakes immediately.