Preheat the oven to 375°F Grease an 8- or 9-inch square baking pan. Put the butter in a skillet over medium-high heat. When the foam subsides, add cocoa powder and semisweet or bittersweet chocolate and stir until smooth. Remove from the heat.
Beat the yogurt and sugar together in a large bowl. Add the butter and chocolate, the semolina, the baking soda, and the vanilla; beat until thoroughly blended. Spread the batter in the prepared pan. Bake until the pudding is lightly browned, about 30 minutes.
Meanwhile, puree the raspberries in a blender or food processor. Depending on how flavorful they are, you may want to add a tablespoon of sugar or a squeeze of lemon juice to the mixture, but taste first to see if either is necessary. Then strain the puree, stirring and pressing the mixture through a sieve with a rubber spatula to leave any seeds behind; be sure to get all the puree from the underside of the strainer.
When the pudding is done, let it rest for a few minutes, then cut it into squares or rectangles and serve warm, on some of the puree, with a few whole berries on top.