Preheat the grill to high.
In a food processor, combine the butter, garlic, jalapeno, parsley, lemon juice, and chives. Season with salt and pepper and process until well combined. Place in a small container. Remove a few tablespoons of the herbed butter and set aside. This reserved butter will be used to finish the lobsters and vegetables once they are off the grill and prevent cross contamination.
Bring a large pot of water to a rapid boil. Place the lobsters in the boiling water and blanch just until the shells turn red, but the meat is not cooked through, about 3 minutes. Remove the lobsters and let cool slightly. Slice the lobsters in half lengthwise. Brush the meat and inside of the lobsters with some of the herbed butter, about 1 tablespoon per lobster half. Place the lobsters on the grill, flesh side down and cook until the meat has grill marks and starts to turn opaque and firm up, about 5 minutes.
While the lobsters are cooking, start the grilled vegetables. Drizzle the vegetables and lemon wedges with olive oil and season with salt and pepper. Place the vegetables and lemon wedges on the grill and brush with some of the compound butter. Grill until tender and browned, about 3 to 4 minutes per side.
Turn the lobsters over and grill an additional 3 to 4 minutes, brushing with more butter, if desired. Remove the lobsters and vegetables to a large platter. Squeeze some of the grilled lemon wedges over the tail meat. If desired, serve with some of the reserved herbed butter.
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