1. Grate the zucchini by hand with a box grater or in a food processor fitted with the shredding disk.
2. Wrap the shredded zucchini in a clean kitchen towel and wring out as much excess water as possible. Repeat a few times, replacing the towel if necessary.
3. Melt the butter in a large skillet over medium-high heat. Add the shredded zucchini and garlic and cook, stirring frequently, until the zucchini is tender, about 6 minutes.
4. Turn the heat down to low; add the heavy cream, salt, pepper and basil and simmer until the cream is absorbed. Taste and adjust seasoning if necessary. Serve warm.