Place all the vegetables and garlic in a large pot and fill with cool water to cover; season with a teaspoon of salt. Bring to boil over medium heat and simmer for about 30 minutes, until the vegetables are very tender.
While the vegetables are cooking, combine the heavy cream, butter, and herbs in a pot and heat over low flame to melt the butter and infuse the herb flavor into the cream - do not allow to boil. Shut off the heat, cover, and let steep until needed. When ready to use, remove the herb stems and the bay leaves.
Drain vegetables and put them into a large mixing bowl. Mash with a potato masher. Stir in the warm cream mixture and mix until the liquid is absorbed and the vegetables are smooth; season with salt and pepper. Put the mashed root vegetables in a serving bowl, garnish with chopped chives and drizzle with a healthy dose of olive oil.