Grate the zucchinis using a box grater or food processor.
Place the grated zucchini in a clean kitchen towel and squeeze out excess moisture.
In a medium bowl, combine the softened butter, grated zucchini, salt, lemon juice, black pepper, thyme, and parsley.
Mix until all ingredients are well combined and the zucchini is evenly distributed throughout the butter.
Transfer the mixture to a piece of parchment paper or plastic wrap and shape it into a log.
Wrap tightly and refrigerate for at least 2 hours or until firm.
Once firm, slice the zucchini butter into rounds and serve on bread, crackers, or vegetables.