Place the beans in a large pot and cover with several inches of water.
Bring to a rolling boil over high heat.
Carefully cut a small slit in the side of the unpeeled onion and tuck the bay leaf inside. Press the clove into the onion.
Add the studded onion, carrot chunks, and thyme sprigs to the pot with the beans.
Reduce the heat to maintain a gentle simmer and cover the pot loosely.
Cook for about 30 minutes, or until the beans begin to soften.
Season generously with salt and pepper.
Continue to simmer, stirring occasionally, until the beans are fully tender but not falling apart, about 45 more minutes.
Add more hot water as needed to keep the beans submerged.
Drain the beans in a colander, discarding the cooking liquid, onion, and carrot.
In a deep skillet large enough to hold the beans, melt the butter over medium heat.
Add the minced shallot and cook, stirring, until it softens and becomes fragrant, about 5 minutes.
Pour in the heavy cream, followed by the cooked beans.
Continue to cook, stirring gently, until the beans are heated through and the cream has thickened slightly, about 10 minutes.
Taste and adjust the seasoning with more salt and pepper if needed.
Garnish generously with fresh parsley and serve immediately.
Don't be afraid to swap the herbs! Fresh tarragon, chervil, or chives make a wonderful substitute for thyme or a lovely addition to the final garnish.
