Preheat the oven to 180ºC.
To make the mayo, place the garlic cloves on a small baking tray and roast in the oven for 30 minutes until soft. When cool to touch, squeeze out the garlic pulp, discarding the outer skin.
Meanwhile, scatter the walnuts onto another small baking tray and roast in the oven for 10 minutes until lightly toasted. Set aside and allow to cool.
Add the egg yolk into the bowl of a food processor or blender. Blend on medium low and add the sunflower oil, then light olive oil in a very fine stream via the feed shoot in the processor lid. Keep whisking until you have a thin, smooth consistency. Add wholegrain mustard, salted capers, anchovy fillets, lemon juice, lime zest and juice, parsley and season to taste with salt and freshly ground black pepper. If the mayo is too thick, add a little more light olive oil. Add walnuts and roasted pulp from 3 garlic cloves. Blend to combine, then transfer the mayo to a serving bowl.
To make the garlic butter, in a small bowl, add the remaining roasted garlic pulp along with the melted butter, extra parsley and extra virgin olive oil, season with freshly ground black pepper.
Using a sharp knife, cut the bugs down the centre horizontally. Heat a barbecue or chargrill pan until smoking. Brush the cut side of the bug liberally with garlic butter then sear cut-side down on the barbecue for 2-3 minutes to heat through.