Start by gathering all your ingredients. Dice the shallots finely and chop any herbs you want to use. Set them aside for later.
In a medium saucepan, melt 4 ounces of the unsalted butter over low heat. It’s important to keep the heat low to avoid browning the butter, as we want it to remain light and creamy.
Once the butter has melted, add the finely diced shallots and sauté gently for 2-3 minutes until they are translucent. Then, stir in the lemon juice, which will add a delightful tang to the butter sauce.
Carefully add the fish to the saucepan, ensuring it is fully submerged in the butter. Poach the fish gently for about 8-10 minutes, depending on the thickness of your fillet. The fish is done when it flakes easily with a fork.
Using a fish spatula, carefully transfer the poached fish to a plate. Drizzle some of the buttery sauce over the top and sprinkle with fresh herbs if desired. Serve immediately and enjoy the decadence!