Preheat oven to 375°F (190°C), crisp potatoes.
Preheat oven to 375°F (190°C) to prepare for the potatoes. Slice the potato into thin rounds and place on a baking try. Line the potatoes flat and spread across in one layer. Drizzle with a little but of olive oil and salt & pepper to taste. Bake for 10-15 minutes, or until potatoes are browned and crisp.
In a small pot, melt the butter over medium heat until it just begins to bubble. Remove the melted butter from heat and discard the white bits as you transfer the butter to another bowl.
Blend egg, lemon, hot water.
In a food processor, blend egg yolks, fresh lemon juice, and hot water. Blend on medium for 5 minutes.
Slowly drizzle butter to emulsify.
Begin to drizzle the warm butter into the mixture through the opening at the top of the food processor as the mixture is on medium. Continue to blend for a couple more minutes until the sauce begins to thicken. When the sauce has thickened, add chopped tarragon and salt to taste. Here’s where you can adjust the taste. Add more tarragon, salt, or lemon juice if desired.
Cook peas in saucepan with butter.
In a small pot, add peas and butter over medium heat and cook until peas are soft, about 10 minutes.
Transfer mixture to a food processor and blend until desired consistency for pureé.
Mix peas with mint, green onion, lemon.
Transfer the purée to another bowl and mix in chopped scallions and mint. Add a squeeze of lemon juice to mixture. Salt to taste.
Poach salmon in court bouillon.
Fill a large pot with ¾ of water and bring to boil over high heat. Add court bouillon ingredients. A court bouillon is quickly cooked broth for poaching, usually to poach fish. Add lemon halves, bay leaves, thyme, black peppercorn, and garlic cloves. Generously salt the court bouillon with kosher salt. Boil for 5 minutes and then turn heat down to simmer. Wait until the liquid gets down to a low simmer until slowly adding salmon fillets in. Poach for 15-20 minutes or until salmon fillet is cooked through. The cooking time will depend on the size of your fillet. Remove salmon from heat and onto a paper towel. Blot salmon with paper towels to get excess liquid out.
Assemble dish by spooning the minted peas onto the center of the dish, then place the salmon filet on top. Drizzle béarnaise sauce over salmon and top with crispy potato chips. Congrats! You just made poached salmon with béarnaise.