Step 1Bring a large pot of generously salted water to a boil. Meanwhile, spiralize the zucchini using the shredder blade. Take up handfuls and cut very long strands into manageable lengths using scissors.
Step 2When the water is boiling, add the greens and quickly soften, about 30 seconds. Immediately strain the greens to a bowl of ice water to stop cooking, then drain, squeezing out excess water and chop coarsely. Set aside. Bring the water back to a boil, add the cabbage, blanch 30 seconds to soften and transfer to the ice water. Drain and set aside.
Step 3Bring the water back to a boil and add the zucchini. Cook for 1 minute to soften, drain, shake off excess water, and set aside.
Step 4In a small bowl, mix together the soy sauce, ¾ teaspoon salt, brown sugar, cornstarch and the chile paste. Stir to dissolve the sugar and salt and set aside.
Step 5Heat a wok or large, heavy nonstick skillet over medium-high heat until a drop of water evaporates upon contact. Swirl in the oil and add the garlic and ginger. Cook, stirring, until the garlic and ginger are fragrant, about 15 seconds. Add the shrimp and cook, stirring, until the shrimp curl and turn pink, about 2 minutes. Add the cabbage and greens and stir-fry until the cabbage is crisp-tender, another 2 minutes. Add the zucchini noodles and soy sauce mixture and stir together until the noodles are heated through and coated with the sauce. Remove from heat, toss with the cilantro and serve with lime wedges on the side.