Add 3½ ounces chopped dark chocolate to a small microwave-safe bowl. Microwave on high in 30-second intervals, stirring between each interval until fully melted (this will likely take a total of 1-1½ minutes). Set the chocolate aside to cool.
Meanwhile, add 1½ cups full-fat or 2% cottage cheese, 2½ Tablespoons granulated sugar, 2 Tablespoons milk, 1 teaspoon vanilla extract, and ½ teaspoon instant coffee granules to the bowl of a food processor (or blender). Blend until smooth, scraping down the sides of the bowl as needed.
While the food processor is running, drizzle in all of the chocolate and continue to process until the chocolate is fully incorporated. Scrape down the sides as well as the bottom of the food processor to make sure no un-blended chocolate remains, and process one more time.
Divide the mousse evenly between 4 small bowls, ramekins, or dessert cups. Cover with plastic wrap and refrigerate until fully chilled, about an hour. Serve cold with desired garnishes.