Place the unsweetened chocolate, dark chocolate chips and butter into a pot set to medium-low heat, and stir until everything is melted. Then remove the  pot from the heat.

Place the eggs and sugar in a bowl and whisk on high with an electric mixer until it forms a ribbon when lifted, about 3 minutes.

Then add the chocolate mixture to the eggs and sugar while whisking. Then sift the flour, baking powder and salt into the bowl and mix just until everything is combined. Then fold in the rainbow chocolate chips.

Line a baking sheet with parchment paper, and place tablespoon-sized balls of batter about 2 inches apart. Stick some more rainbow chocolate chips on top, and bake these for 10-12 minutes at 350F. Allow the cookies to cool for 1 minute, then transfer them to a cooling rack to finish cooling.