Preheat the oven to 350°F (175°C) and line a standard 12-cup muffin tin with paper liners.
In a large mixing bowl, whisk together the gluten-free flour, sugar, cocoa powder, baking powder, baking soda, and salt until thoroughly combined.
Add the egg, milk, oil, and vanilla extract to the dry ingredients. Beat with an electric mixer on medium speed for 2 minutes to develop structure.
Reduce mixer speed to low and carefully pour in the boiling water. Stir until the batter is smooth (the batter will be very thin).
Divide the batter evenly among the 12 cupcake liners, filling each approximately two-thirds full.
Bake for 18 to 22 minutes, or until a toothpick inserted into the center comes out clean.
Cool the cupcakes in the pan for 10 minutes, then transfer to a wire rack to cool completely before frosting.