Using a food processor, add the whole egg and egg yolk, mustard, garlic, and zest of one lime. Blitz to combine.
Pour the oil into a measuring jug and while the food processor is blending, steadily pour a very light stream of oil down the processor’s shoot. Make sure you take your time, this step should not be rushed.
A creamy aioli should slowly start to come together once all of the oil has been added. Finally add the lime juice, sriracha, salt, and pepper to taste. Blend to combine.
Cover and keep in the fridge until ready to serve with fresh beer battered oysters.