Heat the oven to 350 degrees. Spray 24 mini muffin cups with nonstick spray.
In a large bowl, stir beat the brown sugar, butter, egg and vanilla on medium speed until blended. Beat in the graham cracker crumbs, flour and baking soda on low speed.
Shape the dough into 24 1 1/4-inch balls. Place the balls in the muffin cups. Flatten slightly. Bake for 11 to 14 minutes or until the edges are set. Immediately press and indentation into each cookie with the end of a wooden spoon. Cool in the pan for 10 minutes. Remove from the pan to a cooling rack and cool completely (about 15 minutes).
In a medium microwavable bowl, heat the chocolate chips and sour cream on High for 1 minute. Stir vigorously with a whisk until fluffy and smooth (Heat for 10 second longer, stirring vigorously, if needed, until chocolate is melted). Spoon about 1 tablespoon of chocolate filling into each cookie cup. Place the filled cups on a rimmed baking pan.
Move the oven rack to the closest position to the broiler. Heat the broiler. Place a marshmallow half on each cookie cup. Broil for 15 to 30 seconds or just until the marshmallows brown slightly.