Heat the olive oil in a large pot or Dutch oven over medium heat. Add the onion, celery, carrots, salt, and several grinds of pepper and cook, stirring occasionally, for 6 to 8 minutes, or until softened.

Stir in the garlic, then add the broth, half-and-half, gnocchi, thyme, and mustard. Stir to combine, then simmer, uncovered, for 15 minutes, or until the gnocchi is tender.

Add the spinach and stir until wilted. Season to taste and serve topped with a drizzle of olive oil, freshly ground black pepper, red pepper flakes, and parsley, if desired.