Yes, you can. Simply swap the butter for a vegan block butter and add in an extra pinch of salt. When it comes to the egg, this can be left out altogether. Leaving it out results in a flatter cake much more reminiscent of flapjack. It will sink a little in the middle as it cools down, this is normal. It is, however, very delicious - I know because my first few tests of this recipe did not include the egg.