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Step 1
Season the halibut on both sides with salt and pepper.
Step 2
Add the oil to a large frying pan and heat over high heat until it begins to lightly smoke.
Step 3
Place in the halibut, turn the heat down to medium-high, add in 1 teaspoon of butter and cook for 3 to 3 ½ minutes per side or until golden brown and cooked throughout. Remove the cooked halibut and set aside.
Step 4
Add 1 tablespoon of butter to the pan and cook the shallots and garlic over medium heat for 1 to 2 minutes or until very lightly browned.
Step 5
Deglaze with the white wine and cook until there are about 1 to 2 tablespoons of liquid left.
Step 6
Turn the heat off completely and let sit for 1 to 2 minutes before adding in 4 tablespoons of cold butter and mixing until the butter is melted, but not broken. See note on helping to re-emulsify the sauce.
Step 7
Stir in the dill, lemon juice, salt, and pepper, and mix until combined.
Step 8
Pour the sauce over the fish and garnish with more dill and lemon slices.