Prepare a 9x9-inch baking pan by lightly coating with non-stick spray and lining with parchment paper, allowing excess to overhang the pan edges.

Melt butter in a medium saucepan over medium-high heat, stirring occasionally. Watch for foaming and the appearance of brown bits at the bottom, then remove from heat once it has a nutty aroma and amber color.

Add the chopped dark chocolate, cocoa powder, and vanilla extract to the hot butter, stirring until the chocolate is fully melted and the mixture is smooth. Allow to cool for 8-10 minutes.

Using a mixer, whip the eggs and sugar until light and creamy, about 3 minutes.

Gradually pour the cooled chocolate mixture into the egg mixture while continuing to whip until fully incorporated.

Gently fold in the flour until just combined, being careful not to overmix.

Stir in the optional dark chocolate chips if using.

Transfer the batter to the prepared pan, smoothing the top with a spatula.

Bake in the center of the oven for 45 minutes, or until a toothpick inserted comes out with a few moist crumbs. Cool completely in the pan on a wire rack before cutting into squares.