Preheat oven to 350 degrees F (175 degrees C). Grease a shallow baking dish.
Rub the halibut fillets with 1 tablespoon of lemon juice, then season with salt and pepper. Place the fillets into the prepared baking dish, then press the cilantro leaves onto the top of the halibut. Bake the halibut in the preheated oven until the fish flakes easily with a fork, 15 to 20 minutes.
Meanwhile, melt the butter in a skillet over medium heat. Stir in the green onions, red bell pepper, garlic, and red pepper flakes until the vegetables have softened, about 5 minutes. Pour in the white wine, and season with dill and tarragon. Simmer for 2 minutes, then add the chicken broth, half-and-half, Parmesan cheese, and remaining 1 tablespoon of lemon juice; season with salt and pepper to taste. Bring to a boil over medium-high heat, then dissolve the flour into the water, and stir into the boiling sauce. Return to a boil, then reduce the heat to medium-low, and simmer until the sauce has thickened, about 10 minutes. Spoon the sauce over the halibut to serve.