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In a saucepan, cook bacon over medium heat until browning, about 7 minutes. Remove bacon from pan with a slotted spoon and place it in a paper-towel lined bowl. Leave the bacon grease in the pan.
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Melt 1 tablespoon butter in the same pan with the bacon grease over medium heat. Add shallot and celery and cook, stirring occasionally, until softened, about 5 minutes. Add flour and cook for 1 minute, stirring constantly. Add milk, a splash at a time, stirring to incorporate before adding more. When all the milk is mixed in, stir in ½ cup clam juice. Add potato. Bring to a boil. Cover and let simmer over low heat until potatoes are tender, 10 to 15 minutes.
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While the sauce is simmering, cook the clams. Add 1 cup clam juice or water to the bottom of a pot. Add clams. Turn heat to high and cover. Steam until all shells are opened, 5 to 6 minutes. (Keep an eye on it in case the foam bubbles over.) Remove from heat and set aside.
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Season cod with salt and pepper. Melt 1 ½ tablespoons butter over medium heat in a skillet. Add cod to skillet and cook for 4 to 5 minutes. Carefully flip over with a spatula and cook for another 4 to 5 minutes, until fish is opaque and flakes easily. (If you are using thinner cod fillets, they will cook in 3 to 4 minutes per side.)
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Finish the sauce: Once potatoes are tender, add the clams and bacon. You can remove all the clams from the shell, or keep some in the shell and add them to the plate at the last minute for presentation. Stir sauce and cook for one more minute. Taste and add salt and pepper if needed. (I found with the salt from the bacon and brininess from the clams, I didn’t need any more salt.)
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To serve: Divide clam chowder sauce between two bowls. Place cod on top of sauce. Drizzle any melted butter left in the pan over the fish. Garnish with fresh chopped parsley. Finish with a squeeze of lemon juice.