Heat olive oil in a large soup pot or Dutch oven over medium heat.
Add the sausage and break it up with a spoon. Cook until browned and no longer pink (6–8 minutes). Transfer to a plate using a slotted spoon. Leave about 1 tbsp fat in the pot.
Add onion and carrots to the pot. Sauté for 5–6 minutes until softened.
Stir in garlic, oregano, thyme, paprika, and red pepper flakes (if using). Cook 1 minute more until fragrant.
Add diced potatoes and stir well.
Pour in chicken broth and bring to a boil. Reduce to a simmer.
Cook for 15–20 minutes, or until potatoes are fork-tender.
Return sausage to the pot and stir in spinach. Cook 2–3 more minutes until spinach wilts.
Turn off heat. Stir in lemon juice and chopped parsley.
Taste and adjust salt, pepper, or lemon as needed.
Ladle into bowls. Top with grated Parmesan or a drizzle of olive oil if desired.
Serve with crusty bread or a side salad.
