Shred zucchini on the large holes of a box grater to equal about 6 cups. Spread zucchini on a clean kitchen towel; squeeze well to extract most of the liquid.
Heat butter and oil in a large skillet over medium until butter melts. Add zucchini and garlic. Reduce heat to medium-low, and cook, stirring occasionally, until liquid evaporates and mixture is silky and tender, 30 to 35 minutes. Remove from heat, and stir in salt and pepper. Store in an airtight container in refrigerator up to 1 week, or freeze up to 2 months.