Place the potatoes in a medium-size pot, add enough cold water to cover them, then bring them to a boil over high heat.
While the potatoes are cooking, prepare the pesto. Combine the pesto ingredients in a small food processor or blender and blend on medium speed until mostly smooth.
Preheat your BBQ to medium-high heat. Once the potatoes are cool enough to handle, cut them in half and put them into a medium-sized bowl.
Add the red onion, oil, salt, and 2 tablespoons of the pesto and toss to coat. Grill the potatoes and onions for about 5 minutes, until they begin to char.