Preheat oven to 340°F (170°C) and line baking trays with parchment paper.
Roughly chop mini chocolate eggs into 1/4-inch pieces and set aside.
In a large bowl, cream together softened butter, caster sugar, and brown sugar until pale and fluffy, about 2-3 minutes.
Add the room temperature egg and vanilla extract to the creamed mixture and stir until smooth and fully combined.
In a separate bowl, whisk gluten-free flour, baking soda, salt, and xanthan gum until evenly mixed.
Fold the dry ingredients into the wet mixture gently until just combined, then fold in chopped mini eggs and chocolate chips.
Chill the dough in the refrigerator for 45 minutes to prevent spreading.
Scoop dough into golf ball-sized portions and place them on the prepared trays spaced about 2 inches apart.
Bake for 12-15 minutes until edges are set and centers appear slightly underbaked.
Let cookies cool on baking trays for 5-10 minutes before transferring to a wire rack to cool completely.