Preheat the oven to 400 degrees F (200 degrees C).

Mix mushrooms, 1 clove minced garlic, rosemary, and salt together in a bowl. Drizzle olive oil over the mushroom mixture and toss to coat evenly; transfer to a baking sheet.

Roast mushrooms in the preheated oven until golden brown, about 15 minutes.

Meanwhile, melt butter in a large saucepan over medium heat. Stir onions, remaining cloves minced garlic, and thyme into melted butter; cook and stir until onions are completely soft, 7 to 10 minutes.

Combine mushroom mixture and onion mixture in the bowl of a blender or food processor with about 1/2 of the heavy cream; blend on low until combined yet slightly chunky. Return the blended mixture to the stockpot. Stir remaining heavy cream, chicken broth, milk, and black pepper through the blended mixture. Bring the soup to a simmer and cook until the flavors are thoroughly combined, at least 15 minutes.