Preheat your oven to 300 degrees F and line 2 large cookie sheets with parchment paper or silicone baking mats. Set aside.
Add the egg whites to the bowl of your stand mixer, with whisk attachment fixed. Whisk the eggs on medium-high speed just until peaks form, about 3-4 minutes. Taking the caster sugar, add about a teaspoon at a time, fully mixing on medium-high speed, after each addition. Next take your brown sugar, and with the mixer set on low, whisk in the brown sugar. When fully incorporated, increase the speed yet again to medium-high for about 25 seconds. Very gently fold in the frozen raspberries so that they do not break apart and bleed through.
Dollop the meringue about 1 1/2 inches apart on the prepared baking sheets in heaping tablespoons. You may also pipe them if you have the patience and time.
Bake the meringue cookies for 1 hour and 5 minutes or until they are firm. Turn off the oven, but leave the meringue cookies inside. Let cool completely in the oven.
Serve the meringue cookies immediately, or cover them with plastic wrap and refrigerate until you are ready to serve.