Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Toss the broccoli florets and diced potato with the olive oil, sea salt, and black pepper on the prepared sheet.
Roast the vegetables for 20-25 minutes until the broccoli edges are charred and the potatoes are fork-tender.
While vegetables roast, sauté the diced onion and minced garlic in a large pot over medium heat until translucent.
Pour the chicken broth into the pot and bring to a gentle simmer.
Add the roasted broccoli and potatoes to the pot, reserving a few florets for garnish if desired.
Use an immersion blender to partially blend the soup until it reaches your desired level of creaminess.
Stir in the cooked shredded chicken breast and smoked paprika, heating through for 2 minutes.
Remove the pot from the heat and fold in the Greek yogurt until completely smooth and incorporated.
Ladle into a bowl and enjoy immediately while hot.