Crisp bacon in large Dutch oven over medium; transfer to paper-towel-lined plate, reserving 1 tbsp drippings.
Melt butter in drippings; sauté onion 5–7 minutes until soft, then garlic 30 seconds.
Add potatoes and broth; simmer covered 15–18 minutes until potatoes tender.
Mash some potatoes in pot for chunky-thick texture, or blend 1–2 cups for creamier soup.
Over low, add milk, cheddar, salt, and pepper until cheese melts. Gently reheat; do not boil.
Fold in most bacon; reserve some for top and garnish with chives.