Preheat oven to 375 degrees F and line a muffin tin with papers.
Soften the butter in a microwave-safe bowl. Stir in the brown sugar and combine well. Add the eggs and vanilla extract and stir vigorously until thoroughly mixed.
In a separate bowl whisk together the flour, baking powder, baking soda, and salt.
Add the dry ingredients to the wet ingredients and stir until combined.
Stir in the grated zucchini and chocolate chips, reserving a few chocolate chips for the tops.
Using a 3-ounce scooper put the batter into the paper lined muffin tin and place a few chocolate chips on each top.
Bake in a preheated oven for 20-22 minutes, or until the tops are peaked, a little firm, but still a bit soft in the middle. Remove from oven when a toothpick inserted comes out a little sticky, but not wet. Be careful not to over bake.
Allow the muffins to cool in the tin 5-10 minutes, then remove and place them on a cooling rack.
If the edges stick to the tin a bit, just run a butter knife or thin spatula under the edges to loosen, then gently pull them out.
2 cups zucchini is approximately (2) 5" - 6" zucchinis. If you have leftover grated zucchini, just freeze it in a Ziploc bag or an airtight container.
You can also use frozen zucchini, just make sure it's defrosted and drain any excess liquid before adding it to this recipe.