In a large pot over medium heat, add the olive oil and butter. Once the butter has melted, add the diced onion and sauté for 2-3 minutes, stirring occasionally.
Add the chopped broccoli stalks and cook for another 2 minutes, then stir in the minced garlic.
Add the garlic powder, kosher salt, and red pepper flakes. Stir well and continue cooking for another 2-3 minutes, adding another tablespoon of butter if needed.
Pour in the stock and water, then add the fresh thyme. Bring to a gentle boil, then reduce the heat to low and simmer for 10-15 minutes, or until the broccoli is tender enough to mash easily.
Remove the thyme sprig, then use a potato masher or immersion blender to partially blend the soup. I like to leave some small pieces of broccoli for texture rather than blending it completely smooth.
Stir in the pasta (I'm using anelli siciliani) and broccoli florets, then increase the heat to medium. Simmer according to the pasta package directions, stirring occasionally to prevent sticking, until the pasta is al dente and the broccoli florets are tender. Add additional stock or water as needed if the soup thickens too much.
Ladle into bowls, then top with freshly squeezed lemon juice, shaved Parmesan, chopped Italian parsley, a drizzle of extra virgin olive oil, and plenty of freshly cracked black pepper. Enjoy!