Remove papery outer skin from the garlic head (do not peel or separate the cloves). Rub 1 ½ teaspoons oil on garlic head, and wrap it in foil. Bake for 1 hour; let cool 10 minutes. Separate cloves, and peel the skin off of the cloves. Place the garlic cloves in a small dish and set aside.
Soup:
While the garlic roasts, begin chopping and cooking the rest of the soup.
In a large saucepan, heat 1 tablespoon oil over medium-high heat. Add onion, and cook until onion is soft and starting to brown, about 15-20 minutes, stirring occasionally. If onion starts cooking too quickly, add a little water to the pan to slow the cooking.
Add in chopped fresh mushrooms and soy sauce. Cook over medium heat for 10-20 minutes, or until the moisture from the mushrooms disappears.
Add flour and smoked paprika and cook 2-3 minutes until fragrant. Remove from heat.
Allow the garlic to finish roasting, and cool a bit so you can separate the garlic cloves, and peel the skin off of the cloves.
Place half of the roasted garlic in the soup, and reserve the other half for garnish.
Stir the broth into the cooked veggies, and use an immersion blender or a regular blender to purée the soup. Transfer the puréed soup back into the soup pot.
Add the bay leaf to the pureed soup. Bring to a boil, reduce heat and simmer for 10 minutes.
While soup simmers, in a separate sauté pan, add 1 tablespoon olive oil and sauté sliced mushrooms until they start to brown, about 10 minutes.
Add milk and the sautéed sliced mushrooms to the soup, and heat through, about 5 more minutes on low heat.
Remove from heat, remove the bay leaf, and mix in the sour cream. Season to taste with salt and pepper.
Serve, hot, garnished with reserved roasted garlic cloves, fresh rosemary, and additional pepper.