Beat the melted butter, granulated sugar, light brown sugar, and vanilla in a stand mixer on medium speed for 1 minute, then blend in the eggs on low speed. The mixture should look evenly combined, without separate streaks of egg.

Add the flour, corn starch, cocoa powder, baking soda, and salt, and mix on low just until the dry ingredients disappear. The finished dough should be chocolate-colored, glossy, and soft enough to scoop.

Portion the dough into 20 balls using approximately 2 to 2.5 tablespoons per ball, place them on a parchment-lined baking sheet, and refrigerate for 30 minutes while preheating the oven to 350°F. The chilled portions should feel firmer and hold their shape better than the freshly mixed dough.

Arrange the chilled portions about 2 inches apart on a parchment-lined baking sheet and bake for 9 to 10 minutes. Look for just-set, matte edges with centers that still appear puffy and soft.

Leave the baked cookies on their sheet for 3 minutes, then move them to a wire rack to finish cooling. The cookies should become firm enough to lift while retaining a soft center.

Place broken or chopped chocolate in a heatproof bowl, heat the cream in a small pot over medium heat until it begins to simmer, and pour it over the chocolate. Leave the bowl undisturbed for 5 minutes so the chocolate can soften throughout.

Add the vanilla, whisk until smooth, and let the ganache cool for 15 to 30 minutes. The initially thin mixture should thicken to a spreadable consistency similar to peanut butter.

Spread 2 to 3 tablespoons of ganache over each completely cooled cookie, leaving approximately ¼ inch uncovered around the edge, and add the cosmic brownie sprinkles. The frosting should stay on the surface rather than flow over the sides.

Serve the finished cookies or refrigerate them to set the ganache more firmly. The chilled topping should hold its shape when gently touched.