Finely dice the red onion, thinly slice the celery and the garlic. Heat a tablespoon of olive oil in a skillet over a low/medium heat. Add the diced onion, garlic, and celery. Sweat gently for a few minutes until tender and fragrant.
Thickly slice the mushrooms and finely chop the rosemary. Add the sliced mushrooms, rosemary, salt, and pepper to the skillet. Stir well to combine with the softened vegetables. Increase the heat to medium and add the remaining olive oil. Cook the mushrooms until browned all over.
Halve the olives. Add the chopped tomatoes, vegetable stock, olives, and balsamic vinegar to the skillet. Stir to combine. Bring to a gentle boil. Lower to a simmer for 10 minutes to allow the sauce to reduce right down.
While the pasta sauce is cooking, add the zucchini noodles to a large saucepan. Add two tablespoons of water to the pan and a pinch of salt. Set the pan over a medium/high heat and cook the noodles through for just a few minutes until tender. Do not overcook, as the zucchini will become mushy. Drain away all excess liquid.
Divide the zucchini noodles between 2 serving bowls. Divide the pasta sauce between the bowls, mixing into the noodles. Top each bowl with a tablespoon of grated hard Italian cheese.