Cook the noodles in a large saucepan of boiling water until tender, about 6 minutes. Drain.
Meanwhile, heat the oil in a wok over medium-high heat. Cook the onion and garlic, stirring, until softened, about 4 minutes. Add the mince and cook, breaking up any lumps, until browned.
Add the red curry paste and cook for 1 minute. Add the coconut milk, lime juice, fish sauce and zucchini and bring to the boil. Reduce heat and simmer, stirring occasionally, for 5 minutes. Add the peas, spinach and noodles and toss over heat until hot. Serve.