Stock Method
Preheat oven to 400 degrees.
Bring large pot of water to a rolling boil. Add lobsters, return to a boil and cook for 4 minutes.
Remove lobsters and let cool.
Remove claws and tail and set aside.
Place lobster bodies in roasting pan and drizzle with 2 Tbsp olive oil. Put in oven and roast for 45 minutes until slightly charred.
Meanwhile remove meat from claws and tail. Chop meat and reserve in the refrigerator. Discard shells from claws and tail.
Heat 1/4 cup olive oil in large, heavy stockpot over medium heat until shimmering. Add garlic, onions, carrots and fennel, and sauté, stirring frequently for 5 minutes. Add wine, bring to a boil and reduce by half. Add roasted lobster bodies, water and all remaining ingredients. Bring to a boil, reduce heat to low and gently simmer for 1-1/2 to 2 hours.
Let cool and strain through a fine mesh strainer.
Strain again through a cheesecloth for a more refined stock (optional).
Hold stock for use in the risotto or chill or freeze for future use.
Risotto Method
In a stockpot bring lobster stock to a low simmer.
Heat the olive oil over medium heat in a large sauté pan. Add onion and garlic and cook, stirring often, until glossy, about 5 minutes. Stir in rice and cook, stirring, until kernels are slightly translucent, about 3 minutes.
Add wine and cook, stirring constantly, until evaporated.
Add one cup of simmering stock and stir constantly until absorbed by the rice. Add another cup of stock and stir until absorbed. Repeat process of adding stock, stirring and reducing.
In 10 minutes, begin tasting rice. You want it to be tender but with a hint of crunch; it could take 20 minutes or more.
(Tip: Hold risotto at this point by spreading it on a sheet pan and refrigerating. Then reheat and finish just before you are ready to serve.)
Add lobster meat to hot rice and stir for a minute to heat lobster through. And half of the grated cheese and the butter and stir vigorously to incorporate.
Taste and adjust seasoning. Remove from heat and serve garnished with the remaining cheese.
Additional Tips