Preheat oven to 400 degrees F.
Spread frozen broccoli onto a parchment lined sheet pan. Put in the oven for 8 minutes. Remove pan and toss the now thawed broccoli with 2 tablespoons olive oil and 1 teaspoon salt. Roast for 20 more minutes, until broccoli is browning and caramelized.
In a large stockpot, heat 2 tablespoons olive oil to medium heat. Add onion and 1 teaspoon salt. Cook for 6 minutes. Then stir in garlic and potato. Cook for 2 minutes to combine flavors. Add stock, bay leaf, black pepper, and spinach.
With lid on, simmer while broccoli roasts, about 20 to 25 minutes.
When broccoli is finished, add it to the simmering pot of soup.
Add half of the liquid mixture to a blender and puree until smooth. Pour into a separate small stockpot. Then add remaining soup mixture, herbs, and cheese to blender.
Pulse to break down until mostly smooth, but still has a little texture.
Add this to the pureed soup mixture in the smaller stock pot. Add lemon juice, white wine vinegar, and butter.
Stir completely, until all is combined and melted. Taste, and add salt if it doesn’t pop with flavor (this will be depend on how much sodium/salt your chicken broth has).
Add toasted bread hunks and sliced cherry tomatoes to top of each bowl and serve.