Preheat oven to 350ºF (180ºC).
Butter or spray an 8-inch square baking pan. You can line it with a strip of parchment paper, covering the pan's bottom and two sides. The other two sides will remain unlined but greased. This will help you remove the brownies from the pan.
Melt ½ cup unsalted butter with 3 ounces semisweet chocolate in the microwave (at 10-15 second intervals, stirring well each time) or in a double boiler with the bottom of the bowl not touching the water.
Add ¾ cup dark brown sugar and ½ cup white sugar and mix well with a hand whisk. Don't use an electric mixer.
Stir in 2 eggs and combine until it’s creamy.
Add ⅓ cup all-purpose flour and ¼ teaspoon salt and mix to integrate well with a hand whisk.
Add ⅓ cup dark chocolate chips or chunks, ⅓ cup white chocolate chips or chunks, ¾ teaspoon good peppermint extract and ¼ teaspoon vanilla extractMix well until no streaks of flour remain. I use a spatula for this part.
Pour batter into the prepared pan. Smooth the top.
Bake for 20-25 minutes, until a bit puffed and the surface is dry. They still have to be a little jiggly in the middle, and a cake tester or toothpick will come out with very moist (but not wet) crumbs attached.
Let cool completely on a wire rack before lifting the paper carefully so the brownie block comes out in one piece. Place on a flat surface and cut them into squares.
I wrap them and leave them for a day at room temperature before cutting them. It mellows the flavors.