Preheat oven to 375°F; line a small baking sheet with foil. Use a sharp knife to cut about 1/4 inch off top of each garlic head. Place garlic cut side up on baking sheet and drizzle olive oil over heads. Roast garlic until softened, about 45 minutes. Allow to cool slightly. When cool enough to handle, squeeze soft cooked pulp from each clove into a small bowl. (You should have about 1/2 cup soft garlic pulp.)
Melt butter in a large pot over medium-high heat. Add onions and 1 tsp. each salt and pepper and cook, stirring often, until onions have softened, about 4 minutes. Stir in thyme and reserved garlic. Sprinkle in flour. Cook for about 1 minute, stirring, to incorporate flour. Pour in chicken broth, increase heat to high and bring to a boil. Boil rapidly, stirring often, until slightly thickened, about 10 minutes.
Working in batches, puree soup in a food processor or blender. Return to pot and bring to a simmer over medium heat. Add cream, season with salt and pepper and sprinkle with parsley.