Melt the butter in a large Dutch oven or heavy-bottomed soup pot over medium heat. Add the leeks and cook, stirring occasionally, for 10 minutes.
Add the minced garlic and cook, stirring constantly, for 1 minute.
Add the potatoes, broth, bay leaves, and thyme sprigs then season with sea salt and freshly cracked pepper, to taste. Bring to a simmer then reduce heat, cover with a lid, and simmer until potatoes are very soft, about 20-30 minutes.
Remove the bay leaves and sprigs of fresh thyme, then puree with an immersion blender (or regular blender in batches).
Add the heavy cream then taste and add more sea salt and freshly cracked pepper, if needed.
Side Note: If the soup is too thin, simmer uncovered until thickened. If it's too thick, add a bit more broth or water to thin it out.
Ladle into serving bowls and top with bacon bits, shredded Irish sharp cheddar, and chives. Serve immediately. Enjoy.