Heat the olive oil in a large pot over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and cook for an additional minute.
Add the diced carrots and celery to the pot, cooking for another 5 minutes until they begin to soften.
Stir in the cubed potatoes and pour in the chicken or vegetable broth. Bring to a boil, then reduce heat and let simmer for 15-20 minutes, or until the potatoes are tender.
Once the potatoes are cooked, stir in the heavy cream, salmon pieces, dill, thyme, salt, and pepper. Cook for an additional 5-7 minutes, or until the salmon is cooked through.
Remove from heat and stir in the fresh lemon juice. Adjust seasoning if necessary.
Ladle the chowder into bowls and garnish with fresh parsley before serving.