How do I substitute egg in cookie recipe?

I want to make these eggless for a friend, but don't know how. Can I, just like, skip the egg?

This is the only recipe I've ever tried and love it 100%.

recipe--

1/2 cup (100g) butter

an egg (whisked)

1/2 tsp vanilla essence

1 cup flour

1/2 tsp baking soda

1 tsp salt

1 cup dark chocolate

1/2 cup nuts

Melt the butter, add in the sugar while it's still warm. Add in the rest of the wet and (sifted) dry ingredients, mix and freeze the dough (min 1-2 hr). Bake at 180°C for 10-12 min.

Cookies (image and recipe link)

Edited because of stupid mobile typing.