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For the risotto: Fill a large stockpot with enough water to cover the lobsters when immersed. Add salt and bring to a boil over high heat. Place the lobsters, head first, into the boiling water. Bring the water back to a boil, turn down the heat and simmer until the shells turn bright red and the tail meat is firm and cooked through when checked, 8 to 18 minutes.
In high-sided skillet, heat the olive oil and butter over medium-high heat until the butter is melted and foamy. Add the shallots and cook until tender, about 3 minutes.
Add the rice and stir well, making sure all the grains are coated. Stir in the wine, reduce the heat to medium-low and cook for about 2 minutes to reduce slightly.
Slowly start adding the stock, 4 ounces at a time, stirring constantly and giving the rice time to absorb the liquid after each addition. Proceed in this manner until the rice is al dente, about 20 minutes.
Add the chopped lobster meat and the Parmigiano-Reggiano and cook for an additional minute, adding more stock if necessary to prevent the risotto from drying out. Season with salt and pepper.