How to Make It
Preheat the oven to 450°. Bring a very large pot of salted water to a boil. Plunge the lobsters into the water head first and boil just until they stop moving, about 2 minutes. Transfer the lobsters to a cutting board and let cool slightly.
Using a heavy knife, split the lobsters in half lengthwise. Wrap the claws in a clean towel and, using the back of the knife, crack the claws in several spots. Transfer the lobsters, cut side up, to 2 baking sheets.
In a small bowl, mix the dried tarragon with the paprika and a generous pinch each of salt and pepper. Sprinkle the mixture over the lobsters and drizzle with 1/2 cup of the verjus and 1/4 cup of the olive oil. Roast for 12 minutes, until the lobster meat is opaque; transfer the lobsters to a large platter.
Meanwhile, in a small bowl, stir the jalapeños, fresh tarragon, parsley and shallot with the remaining 1/4 cup of verjus and 1/2 cup of olive oil. Season with salt and pepper. Spoon the dressing over the lobsters and serve with the lemon wedges.