Heat the oven to 350°F. Lightly coat a 9x13-inch baking dish with butter.

Unfold ½ (16-ounce) package thawed phyllo dough. Arrange 1 sheet of the phyllo on a work surface with one of the short sides closest to you. Cover the remaining phyllo dough with a piece of plastic wrap to prevent the phyllo from drying out.

Fold the sheet of phyllo like an accordion, making 1-inch folds and going from top to bottom. Place the folded phyllo with a flat side against a short or long side of the baking dish, whichever is closer in length to the folded phyllo. Repeat folding the remaining phyllo 1 sheet at a time and adding to the baking dish, nestling them right next to each other. Spread or fan out the folds of the phyllo in order to evenly fill the baking dish.

Bake until the edges are dried and starting to crisp, about 10 minutes.

Pour 2 sticks melted unsalted butter evenly over the top of the phyllo. Return to the oven and bake until light golden-brown, about 10 minutes. Meanwhile, whisk 2 large eggs, 1 cup whole milk, 1 cup packed light brown sugar, 1 tablespoon vanilla extract, and ½ teaspoon kosher salt together in a large bowl.

Scatter ½ cup coarsely chopped pecans evenly over the top. Pour the egg mixture evenly over the phyllo. Return to the oven and bake until the phyllo is golden-brown and crisp and the custard is set, about 35 minutes.

Place the baking dish on a wire rack. Immediately drizzle ⅓ cup maple syrup evenly over the top. Let the crinkle cake cool slightly before serving.