Preheat the oven to 375°F (190°C).
Butter or spray a baking sheet or line with parchment paper.
Melt the chocolate: Place chopped 4.5 ounces semisweet chocolate in a microwave-safe or glass bowl. You can use the microwave (short 10-15-second spurts, stirring well between each one until it's fully melted) or a double boiler with the bowl containing the chocolate not touching the water. In both cases, make sure it doesn't scorch.
Beat ½ cup unsalted butter with ¼ cup white sugar and ⅓ cup brown sugar in a large bowl for about 3 minutes, until creamy.
Add 1 egg beating well. Scrape the sides of the bowl each time.
Add the melted chocolate, ½ teaspoons vanilla, and mix until smooth.
Sift the dry ingredients (2 tablespoons unsweetened cocoa powder2 tablespoons unsweetened cocoa powder, 1 ¼ cups all-purpose flour, ½ teaspoon baking soda and ¼ teaspoon salt) before adding them to the butter mixture, or have them measured and sift as you add them.
Don’t overbeat at this point. Simply mix well with a spatula or beat at the lowest speed until no streaks of flour remain.
Add ½ cup semisweet chocolate chipsand fold with a spatula to incorporate. At this point, you can bake the cookies or cover the bowl and refrigerate the cookie dough for a day or two.
Scoop portions on the prepared baking sheets making sure they're separated 2 inches from each other.
Bake for 10 minutes, until the edges are dry but the centers are still soft.
Let cool on a wire rack for about 5 minutes and carefully remove from the sheets and let cool completely on the cooling racks.
Store in an airtight container or cookie jar.