Preheat the oven to 375 degrees F. Lightly coat a 9-by-13-inch baking pan with butter.
Whisk together the butter, brown sugar, granulated sugar, eggs and vanilla in a large bowl until smooth. Whisk together the flour, baking soda and salt in a medium bowl. Stir the flour mixture into the butter-sugar mixture. Stir in 2 cups of the chocolate chips.
Spread the batter in the prepared pan. Bake until the edges are light brown and set, about 45 minutes. Cool slightly.
Preheat the broiler. Cover the cookie bars with the marshmallows and remaining 1 cup chocolate chips. Broil at least 8 inches from the heat until the marshmallows turn golden brown, about 2 minutes. (Watch carefully to make sure the marshmallows toast but don?t burn.) Cool and then cut with a sharp knife.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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