Prepare the baking dish by lining an 8×8-inch baking dish with parchment paper, allowing edges to overhang.

Combine 2 cups semi-sweet chocolate chips, ½ can sweetened condensed milk, and 1 tablespoon butter in a microwave-safe bowl. Microwave in 30-second intervals until melted and smooth, about 1 to 2 minutes. Stir in ½ teaspoon vanilla extract.

In another microwave-safe bowl, mix 1 cup white chocolate chips, the remaining ½ can sweetened condensed milk, 1 tablespoon butter, and 1½ cups mini marshmallows. Microwave in similar intervals until melted, about 1 to 2 minutes. Stir in ½ teaspoon vanilla extract.

Pour half of the chocolate mixture into the lined baking dish. Dollop marshmallow mixture on top, then pour remaining chocolate mixture over. Top with additional marshmallow dollops.

Use a toothpick or knife to swirl through the layers, creating a marbled pattern. Chill in the refrigerator for at least 2 hours, or until firm. Lift from the pan using parchment paper and cut into squares.