1 Prepare the zucchini: Slice each zucchini down its length using a vegetable peeler or on a mandolin, creating long, thin ribbons. Stop when you get to the core, which doesn't peel well (and eat it as a snack!).
Lay the noodles out on paper towels in a single layer and sprinkle them with salt. Leave them to “sweat” for about 10 minutes.
2 Melt the butter and steep the garlic: In a large skillet over medium heat, melt the butter. Tilt and swirl the pan gently to move the butter around. The butter will foam a bit, then begin to smell nutty and turn amber with small brown solids on the bottom.
Once this happens, immediately pour butter into a heat-proof bowl, jar, or cup. Use a spatula to scrape all of the browned bits into the bowl. Add the minced garlic to butter and set aside.
3 Season the shrimp: Pat the cleaned shrimp with a paper towel to remove any excess moisture, then toss them with a heavy pinch of salt and 1/4 teaspoon pepper in a large bowl.
4 Cook the shrimp: Wipe the skillet used to melt the butter clean. Return it to medium-high heat. When the skillet is hot (but not smoking) add just enough oil to coat the bottom of the pan.
Working in batches, cook the shrimp for about 2 minutes on each side. They should be pink and opaque, but not curled up too tightly. Transfer to a plate.
5 Cook the zucchini noodles: Pat the excess moisture from the noodles. Place the skillet back over medium high heat, and add a bit of cooking oil (just enough to coat).
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.
Remove the pan from heat.
6 Toss everything together and serve: 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. Transfer to a serving platter or individual plates. Top with fresh parsley and serve.