Melt the butter with the olive oil in a large Dutch oven over medium heat. Add the sliced leeks with a pinch of salt and cook, stirring occasionally, for 8 to 10 minutes, until soft and translucent but not browned.
Stir in the minced garlic and cook for 60 seconds, just until fragrant.
Add the chopped parsnips, stock, bay leaf, thyme sprigs, 1 teaspoon salt, and black pepper. Bring to a boil, then reduce to a gentle simmer.
Simmer uncovered for 20 to 25 minutes, until the parsnips are completely fork-tender.
Remove the bay leaf and thyme stems. Using an immersion blender, blend the soup directly in the pot in short 15-second pulses over about 90 seconds total, until glossy and smooth.
Stir in the cream and lemon juice. Taste and adjust salt as needed. Ladle into bowls and garnish with chives and crispy leeks or extra cream.