It's easier to boil live lobsters whole, as we've done here, but Michael Tusk cuts off the lobster heads and sautés them raw in olive oil to give the pasta sauce a more intense flavor.Plus: More Pasta Recipes and Tips
Bring a large pot of water to a boil. Add salt, then add the lobsters head first and cook them until red all over, about 5 minutes. Transfer the lobsters to a large bowl and let cool to room temperature. Twist off the tails and claws. Using scissors, cut down the backs of the tails and remove the tail meat; then remove the intestinal veins. Crack the claws and knuckles and remove the meat. Slice the lobster tails crosswise 1/4 inch thick and coarsely chop the claw and knuckle meat; cover and refrigerate. Tear the heads into large pieces and reserve with the other shells.
Heat 1/4 cup of the olive oil in a large saucepan. Add all of the reserved lobster shells and cook over moderately high heat, stirring occasionally, until they start to brown, about 8 minutes. Add the fennel stalks, leek, garlic, shallot and 1/2 teaspoon of salt. Cook, stirring, for 2 minutes. Add the tomato paste and cook, stirring, for 2 minutes. Add the wine and stir to scrape up the browned bits on the bottom.
Add the water, parsley and mint sprigs to the saucepan and bring to a boil. Skim the foam off the surface and simmer over moderately low heat for 40 minutes. Strain the stock, leaving the red layer of oil on top. Wipe out the saucepan and return the stock to the pan. Boil over high heat until reduced to 1 cup, about 12 minutes.
Bring a large pot of salted water to a boil. Put the fava beans into a small colander or strainer that fits into the pot. Lower the favas into the boiling water and cook until just tender, about 3 minutes; remove. Add the farfalle to the pot and cook until al dente; drain.
In the same pot, heat the remaining 2 tablespoons of olive oil. Add the peas and favas and warm over moderately high heat for 2 minutes. Add the lobster meat and reduced stock and bring to a simmer. Stir in the farfalle, then the butter to blend and thicken the sauce. Season with salt and spoon the pasta into bowls. Top with the mint leaves and nasturtiums and serve.
The lobster meat, reduced lobster stock and cooked fava beans can be refrigerated separately overnight.
A California Sauvignon Blanc will complement the lobster and play up the clean, fresh flavors of the fava beans and peas.