Warm the olive oil in a large pot over medium heat.
Sauté onion, carrots, and celery with a pinch of the salt until softened, 6–8 minutes.
Stir in garlic, thyme, Italian seasoning, and red pepper flakes. Cook until fragrant, about 1 minute.
Sprinkle in the flour and stir for 1 minute to coat the vegetables.
Slowly whisk in the vegetable broth, scraping the pot. Bring to a gentle simmer.
Simmer 8–10 minutes, stirring occasionally, until slightly thickened.
Add the gnocchi and cook until tender and floating, 3–4 minutes.
Lower the heat. Stir in half-and-half and spinach. Warm gently until spinach wilts.
Stir in Parmesan and lemon juice. Season with remaining salt and the black pepper.
Ladle into bowls and finish with parsley. Serve hot.