Heat a heavy pot or dutch oven ove rmedium heat. Add the butter and when melted, add the onions with a pinch of salt, stirring to coat the onions in fat
Sautee the onions over medium heat, stirring every 5 minutes or so, until the onions soften and brown and then caramelize. Add a bit of water at a time if the onions get too dry and start to stick to the pan or burn (1/4 cup of liquid or more total is fine) This can take 30-40 minutes total
After the onions are caramelized, add the chopped garlic and stir continuously for about a minute. Add the broth, potatoes, salt, and pepper, and stir everything well. Toss in the rosemary and bay leaf. Increase heat to high and bring to a boil, then reduce to low and simmer, covered, for at least 20 minutes or until the potatoes are soft
Fish out any large pieces of rosemary and the bay leaf, and add the lemon juice. Use an immersion blender or batches in a food processor to blend some of the potatoes and create a creamy texture
Ladle into bowls and drizzle with olive oil, some chives, and a bit of minced rosemary if desired