Combine the broth, vinegar, lemon juice and garlic in a small saucepan and bring to a boil. Cook until the liquid is reduced by half, about 2 minutes. Reduce the heat to low and stir in the salt. Swirl in about one-fourth of the butter until it melts; repeat until all the butter is melted. Stir in the lemon zest. Cover the pot and set aside.
Bring a large pot of water to a boil. Add the lobsters, head first, and immediately cover the pot. Bring the water back to a boil and boil the lobsters 10-11 minutes. Use tongs to transfer them to a large bowl and allow them to cool 5 minutes.
Meanwhile, heat the grill for high direct heat.
Working with one lobster at a time, turn it on its back and cut it in half lengthwise. Place the lobsters cut-side down on the grill; grill until just marked, about 2 minutes. Turn and grill another 2 minutes until the shell is charred.
Stir the parsley into the butter and spoon it over the lobsters.
Recipe Notes
Nutrition for each serving: 238 calories, 28 g protein, 2 g carbohydrates, 0 fiber, 8 g saturated fat, 753 mg sodium