Step 1Place the olive oil and butter in a deep skillet and heat over medium heat. Stir in the chopped fennel bulb and cook, stirring, until wilted, about 2 to 4 minutes. Add the orzo and stir to coat the pasta. Pour over the ouzo.
Step 2As soon as the alcohol steams off, stir in the broth and garlic. Bring the mixture to a boil, then reduce the heat and stir until the orzo has absorbed almost all the liquid, 6 to 8 minutes. Stir in the eel, lemon juice and fennel. Stir for a minute, then remove from heat and cover.
Step 3Set the mixture aside for 5 to 7 minutes to absorb any excess liquid. Serve hot, with freshly ground pepper. This makes a scant 2 cups orzo.