In a large pot over medium heat, add the oil, onion, celery, and ½ teaspoon salt and cook for 5 minutes or until softened, stirring occasionally.
Stir in 2 cups broccoli, garlic and red pepper flakes (if using) and cook for 1 more minute, stirring often. Stir in water, potatoes, chicken (if using), and remaining 1 teaspoon salt.
Bring to a boil over high heat, then give it a stir and reduce the heat to low or medium-low and simmer for 12 minutes, stirring and flipping the chicken half way through (if using). If chicken is not cooked at this point, cover with a lid and continue to simmer gently. Transfer the chicken to a cutting board.
To a high-speed blender, add the pumpkin seeds and at least 2 cups of the soup, making sure to get broccoli stems and potatoes in there. Blend until totally smooth, making sure to let the steam escape, then stir back into the pot along with the shredded chicken (if using) and remaining 3-4 cups broccoli.
Simmer for a minute or two or until the broccoli is bright green and fork tender. The broccoli will continue to cook from the residual heat. Turn off the heat and stir in the peas (if using), cheese and lemon.
Serve topped with black pepper, more cheddar (if you’d like), lemon zest (if using), and herbs (if using).