Bring a pot of lightly salted water to a boil. Add the chicken breasts and cook at a low simmer for 10 minutes. Transfer the chicken to a cutting board to cool.
Heat a large pot over medium heat. Add the lemon halves, cut side down and leave them to cook for about 4 minutes. They will be lightly browned. Set them aside.
Add olive oil to the pot, then add the onion. Cook until softened, about 5 minutes. Add the garlic, lemon pepper seasoning, pepper, oregano, and red pepper flakes and cook for 1 minute.
Pour in the broth and whisk up the browned bits from the bottom of the pan.
Bring soup to a boil. Add the orzo and beans. Boil until orzo is tender, 8 to 10 minutes.
When the chicken is cooled enough, shred it.
When orzo is done, add the chicken to the pot and turn off the heat.
Add the greens to the pot and stir until wilted and incorporated.
Squeeze the lemon halves into the soup (being careful not to add seeds).
Season to taste with salt and pepper. Serve with Parmesan.