Melt the butter in a large Dutch oven or heavy-bottomed pot over medium heat. Add the onion and cook, stirring occasionally, until softened and translucent, about 5 minutes.
Stir in the garlic and cook for another minute until fragrant — it should smell sweet, not bitter. If the bottom starts looking dry, add a splash of broth to deglaze.
Add the carrots, pepper, thyme sprigs (leaves and stems intact), and chicken broth. Bring to a boil, then reduce to a steady simmer. Cook until the carrots are fork-tender, about 15 minutes.
Remove the pot from heat and let it sit for 2 minutes — this keeps the thyme from overcooking while you prep the next step.
Working in batches if needed, transfer the soup to a blender or use an immersion blender directly in the pot. Blend until smooth. If using a countertop blender, hold the lid down with a folded towel and let steam escape — hot soup can pop its lid right off.
Pour everything back into the pot (if you used a blender), then stir in the heavy cream, apple cider vinegar, flaky sea salt, and nutmeg. Taste before adding more salt — the broth's sodium level varies by brand. Let it warm through for 2 minutes over low heat. Do not let it boil after adding the cream or it will curdle slightly.
Ladle into bowls and finish with a crack of black pepper on top, if you want it. Serve immediately.
