With the rack in the center position of the oven, preheat to 375 degrees F. Lightly coat a standard muffin pan (with 12 cups) with nonstick spray or use paper liners.
Place a medium heat-proof bowl over a pan of simmering water. Add butter and half of the chocolate. Heat gently, stirring often, until the chocolate is almost completely melted. Remove from heat and continue stirring, allowing the residual heat to melt the chocolate the rest of the way. Let the mixture cool for 5 minutes.
Meanwhile, in a large mixing bowl, whisk together the flour, granulated sugar, cocoa powder, baking powder, baking soda, and salt. Set aside.
To the bowl with the cooled chocolate, whisk in the coffee, yogurt, egg, vanilla extract until smoothly combined. Pour the wet mixture into the bowl with the dry ingredients. With a rubber spatula, stir to combine. Stop as soon as the flour disappears.
Stir in the remaining chopped chocolate. Divide the batter evenly between the 12 muffin cups.
Bake the muffins for 16-20 minutes, until a toothpick inserted into the center of a muffin comes out clean without any wet batter clinging to it. Place the pan on a cooling rack and cool in the pan for 5 minutes, then carefully unmold the muffins and transfer them to the rack to finish cooling completely. Serve warm or at room temperature.
TO STORE: Line the bottom of an airtight storage container with a paper towel and place the muffins in a single layer on top. Add another paper towel on top of your muffins to absorb the excess moisture. Store at room temperature for up to 4 days.
TO REHEAT: You can enjoy these muffins at room temperature or reheat them in the microwave until warm.
TO FREEZE: Wrap the muffins individually in plastic, and store them in a ziptop bag. Freeze for up to 2 months. Let thaw at room temperature or reheat in the microwave.