Soak your wooden skewers in cold water for one hour, before you plan on preheating the grill.
When you have washed and cut your vegetables for the skewers, toss them gently in some sunflower oil and add a few pinches of Kosher salt.
When your assorted vegetables are lightly oiled and salted, assemble your vegetable skewers with an alternating arrangement of the sliced vegetables, and then set them aside for when you are ready to cook.
For the lobster, bring a very large pot of generously salted water to a boil, and prepare an ice bath.
Boil the live lobsters for roughly 4 minutes, depending on the size.
*You may need to boil them two at a time, depending on the size of your largest pot.
Remove the partially-cooked lobsters from the boiling water, and plunge them in the prepared ice bath.
*Boiling the lobsters in advance helps the meat pull away from the shell before it goes on the grill.
When you are ready to start cooking, preheat your grill to 500F.
Melt 12 Tablespoons of butter and add a pinch of Kosher salt.
When melted, remove the butter from the heat.
Cut into the lobster tails on the softer underside, and pour ¼ of the melted butter inside the shell over the exposed meat.
Prepare a finishing vinaigrette for the vegetable skewers by combining the Extra virgin olive oil, a minced garlic clove, chopped parsley, sliced mint, Kosher salt, and freshly-ground black pepper, to taste.
Set the vinaigrette aside for when the vegetable skewers are fully cooked.
Grill the skewers first, as they will take the longest. Grill the skewers until lightly charred on the outsides.
Grill the lobsters on their backs (with the cut-side of the lobster tail facing the sky) for roughly 3 minutes, or until the tail meat is just cooked through.
When perfectly cooked, serve the grilled lobsters with the remaining melted Butter, in addition to the vegetable skewers.
Drizzle some of the herb vinaigrette onto the vegetable skewers.