Slice each zucchini down its length using a vegetable peeler or on a mandolin, creating long, thin ribbons.
Heat olive oil and 2 tablespoons of butter in a large pan or skillet. Add garlic and sauté until fragrant. Then add the shrimp, season with salt and pepper to taste and sauté for 1-2 minutes on one side (until just beginning to turn pink), then flip. Transfer to a plate.
Pat the excess moisture from the noodles. Place the skillet back over medium-high heat, and add a bit of cooking oil.
Toss the zucchini gently in the pan so that it just begins to lose its stiffness. You want it to be al dente, just like pasta. The whole process shouldn’t take more than 3 minutes.
Whisk lemon zest and juice into the brown butter and garlic. Off the heat, add the shrimp back to the pan with the zucchini and pour the lemon-garlic butter over top.
Toss to combine. Top with fresh parsley and serve.