Preheat your oven to 350 degrees Fahrenheit. Line two large baking sheets with parchment paper or silicone baking mats to prevent the marshmallows from sticking to the surface once they melt and caramelize.
In a large mixing bowl, combine the creamy peanut butter and light brown sugar. Use a hand mixer or a sturdy spatula to beat them together until the mixture is smooth and pale. This step ensures the sugar is evenly distributed for a consistent texture.
Add the egg and the alcohol-free vanilla extract to the peanut butter mixture. Continue to mix until the egg is fully incorporated and the batter looks glossy and well combined.
Sift in the gluten-free flour blend, baking soda, and salt. Gently fold these into the wet ingredients until no streaks of flour remain. Be careful not to overmix, as you want the cookies to remain tender and soft rather than tough.
Gently stir in the mini marshmallows using a spatula. Distribute them evenly throughout the dough so that every cookie gets a generous amount of gooey marshmallow goodness. If the dough feels too soft, you can chill it in the refrigerator for ten minutes before scooping.
Scoop rounded tablespoons of dough onto the prepared baking sheets, spacing them about two inches apart. Bake for 8 to 10 minutes. The cookies are done when the edges are golden brown and the marshmallows have puffed up and slightly browned. Let them cool on the pan for at least five minutes before moving them to a wire rack.