Prepare zucchini noodles. Line a baking sheet with several paper towels. Spread your zucchini noodles across the paper towels in an even layer and sprinkle with salt, approximately 1 teaspoon. Toss to coat. Allow zucchini noodles to drain for 30 minutes. After 30 minutes have passed, gather noodles in a clean tea towel and gently (not too hard as this will actually cause the zucchini to turn mushy) squeeze any remaining water out from the noodles. Some remaining water is ok.
Sauté the aromatics. Heat a large skillet over medium-high heat. Once the pan is hot add the tablespoon of olive oil and butter. Allow butter to melt. Reduce heat to medium and add the minced garlic and fresh parsley. Cook, stirring continuously, for 30-60 seconds.
Cook the zoodles. Add the zucchini noodles to the skillet and toss to coat with the olive oil and garlic mixture. Continue to cook, mixing frequently, for 2-3 minutes, or until al dente (see notes).
Add remaining ingredients and serve immediately. Stir in the grated parmesan cheese and immediately remove from heat. Sprinkle with black pepper, salt (if needed), and fresh lemon juice, if desired. Best if enjoyed immediately.
What part of the zucchini the zoodle has come from will (partly) determine cooking time. For example, any zoodles made from the seedier center will cook faster and tend to be mushier. In general, if I see that those zoodles start to look well-done, I will immediately remove the pan from the heat.