In an enameled (non-reactive) 5- to 6-quart soup pot or Dutch oven, heat oil and butter over medium heat until butter foams. Add the onions and cook, stirring occasionally, until onions are soft and translucent but not brown, about 8 minutes. Add garlic and sun-dried tomatoes and cook for another 2 minutes. Add the flour and cook, stirring for 2 minutes. Stir in broth, canned tomatoes (crush lightly with spoon if using whole), honey, thyme, and 1/2 teaspoon salt and 1/4 teaspoon pepper. Bring to a simmer over medium-high heat, stirring often. Reduce the heat to low, cover, and simmer for 30 minutes. Let cool briefly and then purée with a stick blender, or in two or three batches in a standing blender or food processor. Return soup to the pot, if necessary, and turn heat to low. Add mascarpone cheese and stir until melted and fully incorporated. Season to taste with salt and pepper.

Preheat oven to 350ºF. Line a baking tray with foil or parchment. Remove loose papery outer skin from garlic bulbs, but don’t separate cloves. Cut off top of garlic bulbs, exposing ends of individual cloves. Place both heads of garlic, cut side up, onto a square of foil and drizzle with a half tablespoon of oil on each. Tightly cinch up the foil and roast for 30 to 40 minutes until heads are light brown and very soft. Set aside until cool enough to handle.

Squish roasted cloves out of the skins into a medium bowl. Add cheeses, butter, salt and pepper. Mix until combined.

Switch oven to broil and place rack 5 to 6 inches from heat. Evenly spread the cheese mixture onto bread slices. Place slices on lined tray, cheese-side up and broil until cheese is melted and browned in spots, about 3 to 5 minutes. Remove from oven, scatter with herbs and serve with soup.