To clean the strawberries, use a damp paper to wipe each one off. Remove the stems and cut each one in half, lengthwise.
One by one, gently slide each strawberry half onto a metal or wooden skewer (if you're using wooden, soak them in water for about 10 minutes first). Between each strawberry half, slide on one or two basil leaves. Set aside.
In a small mixing bowl, whisk together the honey, vinegar, vanilla and a pinch of sea salt. Set aside.
Preheat a stove-top grill or your barbecue and drizzle or brush a bit of grape seed oil onto the flat surface of each strawberry. Once the grill is hot, place the strawberry skewers on it, flat side down. You should hear a sizzling sound -- if you don't the grill is not hot enough. Wait until it is! Grill until each side is marked from the grill, about 30 seconds per side. Place the skewers on a plate and while they're still hot, use a pastry brush to add the glaze to the kebabs. Remove them from the skewers to serve.