Place frozen raspberries, sugar, and water in a small saucepan. Heat over medium-low heat until the raspberries soften and the sugar dissolves completely. Cool slightly and then transfer to a blender or food processor; puree until smooth. Strain through a fine-mesh strainer to remove seeds. Set aside.

Preheat oven to 350 degrees F. Generously spray a donut pan with nonstick cooking spray.

In a medium bowl, whisk together flour, cocoa powder, sugar, baking powder, baking soda, and salt.

In another medium bowl, whisk together yogurt, milk, egg, vanilla, and melted butter. Whisk in ¼ cup plus 2 tablespoons raspberry puree.

Pour the wet ingredients into the bowl with the dry and stir gently until just combined.

Scoop the batter into a quart-size zip-top bag: Fold the top opening of the bag down and over itself (to the outside) and set the bag in a cup or mug, so that you can scoop the batter into one corner of the bag. Scoop batter into the bag, remove it from the cup, and unfold the rim of the bag. Twist the top of the bag a few times so that it looks like a piping bag, and cut off the bottom corner of the bag. Pipe the batter into the six wells of the prepared donut pan.

Bake donuts for 9-10 minutes, until they are set and tops bounce back when gently pressed. Let cool in pan for 5 minutes, then transfer to a wire rack set over a rimmed baking sheet (to catch glaze drips) to cool for 10 minutes more.

Whisk together powdered sugar and raspberry puree until smooth. Heat glaze in microwave for 20 seconds; stir until smooth. Immediately dip each donut into the glaze and set back on wire rack. Let the glaze set for 5 minutes. Re-warm glaze in the bowl by microwaving for 20 seconds, stirring, and microwaving 15 seconds more until smooth. Working quickly, spoon a second layer of glaze onto each donut as needed. Re-warm the glaze as needed between donuts.

Sprinkle with sprinkles, if desired. Let glaze set on donuts before serving. Donuts are best served the day they are made.