Heat the olive oil in a large stockpot or Dutch oven over medium heat.
Add the diced onion and cook for approximately 5 minutes, stirring occasionally, until softened and translucent.
Add the chopped garlic and red chili flakes. Cook for another minute, stirring frequently so the garlic doesn't burn.
Add the cubed potatoes and broccoli florets to the pot.
Pour in the vegetable stock, then season with salt and black pepper. Stir everything together.
Increase the heat and bring the soup to a boil. Reduce to a gentle simmer, cover, and cook for approximately 25 minutes, or until the potatoes and broccoli are very tender.
Remove the pot from the heat. Using an immersion blender, carefully blend the soup until mostly creamy while leaving some pieces of broccoli and potato intact for texture.
Return the Broccoli Feta Soup to a gentle simmer.
Stir in the ditalini and cook according to package directions, approximately 10–12 minutes, until al dente. Stir frequently, particularly toward the end, to prevent the pasta from sticking to the bottom.
Once the pasta is tender, remove the pot from the heat.
Stir in the crumbled feta and chopped fresh parsley. Mix gently until the feta begins to soften into the hot soup.
Taste and adjust the salt, black pepper, or chili flakes as necessary.
Ladle into bowls and finish with additional crumbled feta, parsley, black pepper, or red chili flakes before serving.