Season fish fillets with salt and pepper. Heat olive oil in a pan over medium-high heat. Fry fillets 3-4 minutes per side until cooked through. Cut into bite-sized pieces in the pan. Transfer to a plate and drizzle with lemon juice. Keep warm.
Peel and finely dice carrots and onion. In the same pan, sauté over medium heat for 3-4 minutes until softened. Add thawed spinach and sauté for 1-2 minutes. Pour in white wine and scrape up any browned bits. Add cream and simmer for 8-10 minutes until sauce reduces by roughly one-third. If needed, mix cornstarch with a little warm water and stir into sauce until creamy.
While sauce simmers, bring a pot of water to a boil. Gently add eggs and boil for 8-9 minutes. Transfer to ice water to cool, then peel and quarter.
Add fish pieces to sauce and season with salt, pepper, and dill to taste. Simmer over low heat for 5 minutes.
Divide sauce and fish onto plates. Arrange quartered eggs in the center of each plate.