Grease a 9x13-inch baking dish with butter or non-stick spray to prepare for the brownies.
In a microwave-safe bowl, melt 3/4 cup unsalted butter and 1/4 cup creamy peanut butter in 30-second intervals, stirring until smooth.
In a large mixing bowl, combine the melted butter and peanut butter mixture with 1 cup granulated sugar. Stir in 2 slightly beaten eggs and 1 teaspoon vanilla extract until smooth.
In another bowl, mix 2 1/2 cups graham cracker crumbs and 1 cup semi-sweet chocolate chips. Gradually add this to the wet mixture, stirring well.
Gently fold in 2 cups miniature marshmallows until evenly distributed.
Transfer the mixture to the prepared baking dish and press down evenly with a spatula to compact.
Melt the additional 1 cup semi-sweet chocolate chips in a microwave-safe bowl and drizzle over the brownie mixture evenly.
Microwave the remaining 1/4 cup peanut butter until pourable and drizzle over the melted chocolate for a decorative finish.
Refrigerate the brownies for at least 2 hours until firm and set.
Cut into squares, serve, and enjoy your delicious no-bake brownies!