Place the lobster broth in a saucepan and bring it to a simmer. Reduce the broth to a sauce consistency, about 1 cup. Set aside in the pan.
Cook the orzo as you would pasta, in lightly salted water until just barely cooked. Pour the cooked pasta into a strainer to drain and rinse under cold water. Shake the strainer to remove excess water and add the cooked orzo to the lobster broth.
Heat the orzo and lobster broth. Bring to a simmer. Add the mascarpone and season with salt to taste. Let it simmer for 1 minute, then remove the pan from the heat and keep warm.
Meanwhile, place the lobster pieces in one layer in a saucepan. Pour in the Beurre Monté; the lobster should be almost covered. Heat gently to warm the lobster.
To serve, stir the chives into the orzo. Pipe a circle of coral oil in the bottom of each serving dish. Place about 1/3 cup of orzo in the center of the oil, allowing it to spread the oil out into a larger circle. Arrange a piece of lobster tail and claw in the center of the orzo and top each serving with a Parmesan crisp.