Start by shredding your zucchini using a fine grater. Place the shredded zucchini in a clean kitchen towel or cheesecloth and gently squeeze to remove excess moisture. Set aside.
In a medium saucepan over medium heat, melt the unsalted butter. Stir continuously until it foams and turns light brown, releasing a nutty aroma. Remove from heat and let cool slightly.
In a large mixing bowl, combine the browned butter and brown sugar. Stir until the sugar is mostly dissolved and the mixture is smooth.
Add the vanilla extract and eggs, one at a time, mixing well after each addition until the mixture is glossy and well combined.
In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, folding gently with a spatula until just combined.
Fold in the shredded zucchini and butterscotch chips until evenly distributed.
Preheat oven to 350°F (175°C). Line an 8x8-inch baking pan with parchment paper or lightly grease it. Pour batter into the pan and smooth the top.
Bake for 25-30 minutes, until edges are golden and a toothpick inserted in the center comes out with a few moist crumbs.
Allow blondies to cool completely in the pan on a wire rack before cutting into squares. Serve and enjoy.