For the Salmon with Lemon Caper Butter Sauce:

1. Allow the salmon to rest at room temperature for 10 minutes prior to cooking to remove some of the chill.
2. Heat oil in a large skillet over medium-high heat. Once shimmering, lower the heat to medium.
3. Add the salmon, skin-side down pressing down gently for a few seconds to ensure that the skin makes full contact with the pan. Cook 4-6 minutes or until the salmon easily parts with the pan, then flip flesh-side down. If the salmon resists, keep cooking for another 30 seconds and try again; it should not stick.
4. Cook for 2-4 more minutes or until the salmon has reached your desired internal temperature. 120 degrees Fahrenheit / 49 degrees Celcius is medium-rare, 130 degrees Fahrenheit / 54 degrees Celcius is medium, and 145 degrees Fahrenheit / 63 degrees Celsius is well-done (and considered fully-cooked).
5. Carefully wipe the pan out with a paper towel.
6. Add the butter, garlic, and shallot. Cook until translucent, then add capers, lemon juice and zest, kosher salt, and pepper. Cook until warmed through, then serve over top of the salmon.

For the Pommes Purée:

1. Add the potatoes to a large pot and cover with water to 1-inch above the potatoes. Salt the water and bring to a boil. Once boiling, lower the heat to maintain a simmer. Simmer for 20 minutes or until the potatoes are fork-tender, then drain.
2. the potatoes are slightly cool, peel the skins off of them. They should slip off easily.
3. Process the skinned potatoes through a potato ricer. If you don't have a ricer you can push the potatoes through a colander or carefully blend with a hand mixer or food processor on low speed; do not overmix.
4. Add the butter, cream, and thyme back to the pot you boiled the potatoes in and bring to a low simmer over medium heat. Add the processed potatoes to the pot and gently fold the potatoes in until they emulsify with the butter and cream. Taste for salt and adjust if necessary. Serve warm.

For the Haricots Verts:

1. Prepare an ice bath and reserve it to the side.
2. Bring 3 quarts of water and the salt to boil a large pot over medium-high heat. Once boiling, add the green beans and cook for 3-5 minutes depending on the thickness of your green beans.
3. Using a pair of itching tongs, transfer the cooked green beans to the ice bath to quickly halt cooking. This helps ensure that the green beans remain vibrant and tender-crisp.
4. Once cooled, drain the green beans well. Serve with the salmon and pommes purée.