Preheat the oven to 350°F (180°C).

Brush off the papery outer layers around each of the heads of garlic, leaving them whole with all of their cloves connected. Trim 1/4 inch (6mm) off the top off each head of garlic to expose the tops of the garlic cloves. Drizzle each head with 1 teaspoon of the olive oil and a pinch of salt. Wrap each head separately in parchment paper, then foil (to allow the garlic to steam and not burn, and to reduce aluminium transfer), and roast them in the oven for 40 to 60 minutes, until tender. Allow to cool, then squeeze out the garlic pulp from the cloves, and set aside.

Fill a large pot with cold filtered water. Add the sliced potatoes with 1 tablespoon of the salt, and bring to a boil. Simmer, uncovered for 5 to 7 minutes until just tender. Drain, and set aside. Wash the pot, and place back on the stovetop.

Over medium heat, warm the olive oil, and sauté the onions with 1/2 teaspoon of the salt for about 30 minutes, until caramelized.  

Add the vegetable broth, increase the heat to high, and bring to a boil. Reduce the heat to medium-low, add the cooked potatoes, roasted garlic, remaining teaspoon salt, and pepper, and simmer gently for about 10 minutes to allow the flavors to mesh.  Remove the pot from the heat, and allow to cool slightly. Stir in 1/2 cup of the parsley and add the lemon juice. Season with salt and pepper to taste.

Pulse very briefly with an immersion blender just to break up some of the potato, but keeping the soup rustic and chunky.

To serve, ladle the soup into bowls and garnish with remaining parsley.