Soften the onion: Melt the butter in a large, heavy pot over medium heat. Add the onion and cook, stirring occasionally, for 5 minutes, until softened but not browned.
Add garlic and thyme: Add the garlic and thyme and cook for 1 minute, until fragrant.
Add parsnips, apples, and broth: Add the parsnips, apples, broth, salt, and pepper. Bring to a boil, then reduce the heat to low, cover, and simmer for 20 minutes, until the parsnips are very tender.
Blend smooth: Remove from the heat. Blend with an immersion blender until completely smooth, or blend in batches in a standing blender with the lid vented, then return to the pot.
Finish with cream: Stir in the cream and warm over low heat for 5 minutes. Taste and adjust the salt. Serve hot, with extra thyme over each bowl.