1. Cook the pasta in a large pot of salted boiling water until al dente. Drain them.
2. Meanwhile, cut the zucchini in half lengthwise, then slice each half into thin slices.
3. Heat the butter and oil in a large skillet and sauté the zucchini with the pressed garlic, stirring constantly, until just tender. Add the vegetable broth and bring to a boil. Reduce the heat, add the cream, grated lemon zest, and chives, and stir until the mixture is hot.
4. Incorporate the pasta into this mixture, stir gently, and serve immediately.