Combine cream, milk, and potatoes in a pot; bring to boil. Reduce to simmer and cook until potatoes are cooked, yet retain shape, 15 to 20 minutes. Remove pot from heat, add smoked haddock, and let it steep.
Meanwhile, heat 1/4 cup oil in a large pot over medium. When it begins to smoke, add bacon and cook until fat renders and bacon has some color, about 2 minutes. Add carrot, celery, onion and 1/2 teaspoon salt; cook and stir about 8 minutes. Add wine and crumble chilies into mixture; c0ok until wine evaporates, scraping bottom of pan to get sticky bits up (It'll all look a bit creamy.) Add stock; simmer until reduced by half. Turn off heat.
Remove haddock and set aside.
Blend about half the potatoes with half the cream mixture until smooth; add to vegetables with remaining potatoes and cream mixture and bring to a simmer.
Remove skin from haddock. Run fingers along flesh, picking out any little bones you feel. Pull fish into bite-size pieces and add to soup. Continue cooking 5 minutes.
Pour in olive oil and about half celery and parsley leaves. Squeeze lemon half into soup. Season with more salt, chilies, and lemon juice. Garnish with remaining celery and parsley and a drizzle of olive oil.