Bring a large, heavy pot filled with a few inches of salted water to a boil. Add the broccoli pieces and boil for five minutes. Drain well.
Add the olive oil and garlic to a wide pan like a braiser over medium heat. After a minute or two, when the garlic starts to soften and turn golden, add the broccoli, season with salt and pepper, and toss together.
Cover the pot, turn the heat down as low as it will go, and cook for about an hour, stirring occasionally, until the broccoli is soft enough that it yields when you press it with the back of a wooden spoon (it may brown a little during this process -- this is a good thing).
Add the vegetable broth, lemon and Bruschetta topping, and return to a boil over medium-high heat. Simmer for 5 minutes.
Using a submersible blender, puree roughly half of the soup - there should still be a fair number of bite-sized pieces of broccoli.
Stir in the nutritional yeast, allspice, and lemon juice. Adjust for additional salt and lemon if needed.
Serve piping hot with a hunk of crusty bread.