In a heavy covered casserole, heat the butter until melted. Add the shallots and sauté until tender. Add the rice and sauté until it becomes opaque; 3 to 4 minutes.
Pour hot broth over the rice, add the bay leaves, parsley sprigs, and zest of 1 lemon. Season to taste and bring the broth to a boil.
Reduce the heat to a simmer, cover, and cook until the liquid is absorbed; about 15 to 20 minutes depending on the depth of your pot.
Heat olive oil in a large skillet and sauté the sliced cabbage until tender and bright green; 3 to 4 minutes. Season to taste.
Stir the cabbage and remaining lemon zest into the rice and taste for seasoning. For serving, top with lemon slices and fresh parsley.