Clean the artichokes: trim the base, peel tough outer leaves, and scrape the fuzzy choke with a spoon. Remove remaining tough leaves and drop each cleaned artichoke into the lemon water to prevent browning. Cut artichokes into halves or quarters.
Place the cut artichokes in a saucepan with 1 cup of the lemon soak water, olive oil, crushed garlic, herbs, and salt. Bring to a boil, cover, and simmer over medium heat until tender, about 20 minutes. Remove with a slotted spoon and reserve 1 generous teaspoon of the cooking liquid with oil for the topping.
Heat the reserved teaspoon of cooking liquid in a skillet. Sauté the sliced garlic briefly until fragrant. Add the cooked artichokes, cherry tomatoes, hazelnuts, and spinach. Cook, stirring, until tomatoes soften and spinach wilts, about 2–3 minutes. Taste and season as needed.
Arrange on plates, scatter Parmesan shavings over the top, drizzle with olive oil if desired, and finish with a pinch of coarse salt. Serve immediately.