In a large, deep skillet or saucepan, pour in the fish or vegetable broth. The pan should be large enough to hold all the cod fillets without overcrowding.
Place the lemon slices and fresh dill sprigs in the broth.
Heat the broth over medium-high heat until it comes to a gentle simmer. Reduce the heat to low to maintain a gentle simmer.
Season the cod fillets with salt and pepper.
Carefully place the cod fillets into the simmering broth. Make sure the broth covers the fillets. If not, you can add a little more broth or water.
Poach the cod for about 5-7 minutes, or until it becomes opaque and easily flakes with a fork. The cooking time may vary depending on the thickness of the fillets.
Using a slotted spatula, carefully remove the poached cod fillets from the broth and set them aside on a serving plate.
In a small bowl, combine the Greek yogurt, lemon zest, lemon juice, fresh dill, minced garlic, salt, and pepper. Mix well until all the ingredients are fully incorporated.
Taste the sauce and adjust the seasoning, adding more salt, pepper, or lemon juice as needed.
Drizzle the lemon dill sauce over the poached cod fillets
Garnish with additional fresh dill and lemon slices if desired.
Serve the poached cod with your choice of side dishes, such as steamed vegetables, rice, or a fresh green salad.