Using either a spiral slicer or julienne peeler, cut the zucchinis into noodles and lay on paper towels. Sprinkle lightly with salt and set aside.
Heat 1 tablespoon of the sesame oil over medium-high heat and add the pork. Cook until lightly browned and remove from pan. Add the remaining oil, followed by the green onions, garlic, and ginger. Cook for 1-2 minutes, until fragrant. Add the carrots, broth, water, coconut aminos, and pepper flakes. Simmer for 10 minutes, until carrots are tender.
Add the pork and the zucchini noodles to the pot and simmer for 5 minutes, until heated through. Serve hot.