Preheat the oven to 425 degrees and move the oven rack to the middle position.
Cut potatoes into ¼ inch slices and toss with 1 tablespoon olive oil. Arrange the potatoes into nests of 12 potatoes. 3 overlapping potatoes per row, 4 rows. Season the potatoes with salt and pepper. Bake potatoes for 35 minutes, until lightly browned and tender.
While the potatoes are cooking, prepare the compound butter. In a small bowl, mix together the butter, lemon zest, garlic, thyme and parsley. Set aside.
Prepare the fish. Season each fillet with salt and pepper. Coat each fillet with ¼ of the compound butter. Cover and refrigerate until potatoes are done cooking.
Once the potatoes have finished cooking, remove from oven and place one fillet on each nest of potatoes. Top each fillet with 2 slices of lemon. Return pan to oven and cook for an additional 15 minutes, or until cod is flaky.
Use a spatula to gently transfer the potatoes and cod to individual plates.
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