Preheat the oven to 410 degrees. Grab a 12-cup muffin tin and spray each mold with non-stick spray. Set aside.
Add 1½ cups of raspberries to a food processor or blender and pulse until the berries are pureed. Press through mesh sieve to remove the seeds. Set puree aside.
Create double-boiler by filling a medium sauce pan with water. Turn the heat to medium. Once it begins to boil, reduce to medium-low and place a large bowl on top. The bowl should rest on top and NOT touch the water.
Cut butter into tablespoons and place into bowl. Place chocolate on top of butter. They should slowly begin to melt. Stir regularly to combine butter and chocolate together, forming a silky smooth chocolate sauce. Remove from heat when completely melted. Let it cool slightly so it's warm, but not hot. Add in raspberry puree.
In a medium bowl, lightly whisk eggs, egg yolk, and vanilla together. Sift powdered sugar into the egg mixture. Add 1/4 cup slightly cooled chocolate to egg mixture and combine. Add remaining chocolate and combine. Do not over mix.
Sift flour into chocolate mixture. Fold flour gently into chocolate mixture with a spatula just until combined.
Grab muffin tin and fill each mold with the cake mixture about 80% of the way. Press a raspberry into the center of the batter until it's full engulfed and hidden. Cover with more batter, if needed.
Place baking sheet with ramekins into preheated oven and bake for 11-12 minutes. The cake will be done when you see that the perimeter is cooked but the center is still wet.
Once they're done, pull them from the oven. Let them sit for 4 minutes. Then, use a sharp knife to cut around the edge to release cake from the muffin mold. Use an offset spatula to gently remove the cake from the tin. Flip the cake upside down onto a serving plate. Sprinkle with powdered sugar and garnish with more raspberries. Serve immediately.