Cook baby potatoes in salted boiling water until tender, about 20-25 minutes. Season with salt, pepper and butter.
Make Pea Sauce: Blanch fresh peas in salted boiling water, until just cooked, about 2 minutes, or until they float. Rinse with ice cold water to shock them and stop the cooking process ( to help them stay green). Place peas in a blender with the rest of the pea sauce ingredients, and blend until very smooth. Place in a saucepan, and do not heat until right before serving.
Saute Mushrooms. Heat olive oil and butter in a skillet. Saute mushrooms and shallots over medium heat, until tender, about 5-7 minutes. Season with salt and pepper, set aside.
Sear the fish. Season both sides of fish with salt and pepper. In a large skillet, heat oil over medium high heat. Once hot, sear the fish, skin side down, until the skin is golden and crispy, about 3-4 minutes. Turn over and cook for a couple more minutes or place in a warm oven- until just cooked through to medium ( or medium rare).
Assemble: Heat pea sauce over medium-low heat, do not boil, just gently heat to keep its color vibrant. Divide the warmed pea sauce among plates. Top with potatoes, then fish. To keep the skin crispy, serve with skin side up. Top with the mushrooms.