Lobster: Bring a large pot of salted water to a boil over high heat. Cook 2 lobsters at a time until three-quarters done, approximately 10 minutes.
Heat 2 large saute pans over high heat. Split the lobsters in half, brush with olive oil and season with salt and pepper, to taste. Place the lobster in the pan, flesh side down and cook until nicely browned. Turn over and cook shell side down for 1 more minute.
Cava-Tarragon Butter Sauce: Place the shallots, Cava and vinegar in a medium non-reactive saucepan. Boil the liquid over high heat until reduced to 2 tablespoons. Whisk in the heavy cream and cook for 1 minute. Reduce heat to medium and add the butter, piece by piece, whisking well after each addition until all has been used. Season with salt and white pepper and add the tarragon.
Risotto: Heat olive oil in a medium saucepan over medium heat. Add onions and cook until soft. Add rice and cook for 2 minutes. Add white wine and cook until completely reduced. Add clam juice or stock and cook until all of the liquid has been absorbed. Add boiling water 1 cup at a time and cook until all liquid has been absorbed by the rice. Repeat until all water is used. Fold in the Salsa Verde and cook until mixture has absorbed most of the liquid. Fold in the herbs and season with salt and pepper, to taste.
Preheat oven to 375 degrees F.
Place tomatillos and garlic cloves on a baking sheet or small roasting pan, toss with the oil and season with salt and pepper. Roast until the tomatillos are soft about 20 to 30 minutes, depending on the size. Transfer the mixture to a food processor with the herbs and process until smooth.
To assemble dish: Spoon risotto onto a plate and top with 1 or 2 lobster halves. Serve the Cava Butter Sauce on the side.