Heat olive oil in a Dutch oven or large pot over medium heat. Add diced onion and cook for 5-6 minutes until softened and translucent. Add minced garlic and cook for another 30-60 seconds until fragrant, being careful not to burn it.

Add mushrooms to the pot, but don't overcrowd them. Cook in batches if necessary. Allow them to release their moisture and then brown, about 5-7 minutes. They should become golden and slightly caramelized.

Stir in tomato paste and cook for about 1 minute, allowing it to darken slightly and coat the vegetables.

Add the canned tomatoes with their juice. Use your wooden spoon to break the tomatoes into smaller pieces.

Pour in the broth and season with salt, pepper, and red pepper flakes if using. Bring to a boil, then reduce heat to maintain a gentle simmer. Cook uncovered for 25-30 minutes, allowing the flavors to develop and the soup to reduce slightly.

Remove the pot from heat and stir in the grated Parmesan cheese until melted and incorporated.

For a partially smooth texture, use an immersion blender to briefly blend some of the soup, leaving plenty of chunks for texture. Alternatively, transfer about half the soup to a standard blender, blend until smooth, then return to the pot and stir to combine.

Taste and adjust seasoning if needed. Ladle into bowls, garnish with additional Parmesan cheese, fresh herbs, and a drizzle of good olive oil.