Cut onions in half lengthwise and peel. Cut each half into thirds, then slice each piece crosswise about 1/4 inch thick.
Heat 1 1/2 Tablespoons olive oil in a 10-inch skillet, add the onions and cook over medium heat, stirring occasionally. When they begin to color, turn heat to medium low, cover and cook for 30-40 minutes, stirring occasionally. After 20 minutes, remove the lid and keep an eye on them to make sure they don't burn.
Meanwhile, prepare the remaining ingredients. Mince rosemary leaves and set aside. Toast walnuts at 350 degrees F for 8-10 minutes, let cool, and finely chop.
When the onions are caramel colored, raise the heat, add the vinegar, stirring constantly. Season with 3/4 teaspoon salt, 1/4 teaspoon pepper, 1/4 teaspoon ground cloves, and minced rosemary. Remove onions from the pan.
In a large saute pan (you can use the same pan you did for the caramelized onion), add 2 teaspoons olive oil. Add zucchini noodles and cook for 3-6 minutes, until bright green and still a little crisp. Add most of the caramelized onions back to the pan, along with the toasted walnuts. Toss together and immediately remove to a serving plate.
To serve, top with remaining caramelized onions, and sprinkle with cheese.