Prepare the Vegetables: Heat olive oil in a large pot over medium heat. Add chopped fennel and sliced leeks, sautéing until they become translucent and tender, about 5-7 minutes.
Add Garlic and Seasonings: Stir in the minced garlic, salt, and black pepper, continuing to cook for another 2 minutes until the garlic is fragrant.
Pour in Broth: Gradually pour in the broth, scraping any bits off the bottom of the pot. Increase heat to bring the mixture to a gentle boil.
Simmer the Soup: Reduce heat to low and let the soup simmer for 15 minutes, allowing the flavors to meld.
Blend Soup: Using an immersion blender, carefully blend the soup until smooth. Alternatively, you can transfer the soup to a blender in batches and blend until smooth, then return to pot.
Add Heavy Cream: Stir in the heavy cream and bring the soup back to a simmer. Adjust seasoning if necessary.
Cook the Salmon: While the soup simmers, season the salmon fillet with a pinch of salt. In a separate pan, melt butter over medium heat. Add the salmon and cook for 4-5 minutes on each side or until it flakes easily with a fork.
Flake the Salmon: Once cooked, transfer the salmon to a plate and flake it into bite-sized pieces with a fork.
Finish the Soup: Stir in the fresh dill, lemon zest, and lemon juice to the soup. Add the flaked salmon to the pot and gently stir to combine.
Serve Warm: Ladle the soup into bowls, garnish with additional dill if desired, and serve warm.