Preheat the oven to 400 degrees F. Cut two long pieces of parchment paper, each about 18 inches long.
In a small mixing bowl, mash together the butter, shallot, dill, and lemon zest. Add salt and pepper to taste.
Prepare the parchment packet by placing half of the veggies on one side of the parchment paper. Place a cod fillet on top of the veggies, followed by half of the shallot butter. Put lemon slices on top of the fillet. Sprinkle with salt and pepper, and add some fresh sprigs of dill if desired. Fold the other side of the parchment paper on top of the veggies and fish and roll in the edges to form a packet. Repeat with the other piece of parchment and the rest of the ingredients. The packets should look like large potstickers.
Transfer the packets to a baking sheet and then to the oven. Let them bake for approximately 15 to 18 minutes. For reference, cod needs about 8 to 10 minutes of baking time per inch of thickness, so you may need more or less cooking time depending on the size of your fillets.
Remove the baking sheet from the oven and slice open the packets with a knife (or tear with your fingers). Some steam will escape, so be careful. Eat your meal right out of the packet or transfer the fish and veggies to a plate. Enjoy!
You can sub other veggies, but they need to be soft and thin, like cherry tomatoes, green beans, or sliced onions.
The parchment packets can be prepared up to 3 hours in advance. Keep them in the fridge until you're ready to turn on the oven.
Serve this meal on its own or with a whole grain or potato salad.