Preheat oven to 350ºF (180ºC).
Butter or spray an 8-inch square pan and line it with a strip of parchment paper that covers the bottom and two sides. This will help remove the baked brownies.
Put 10.5 ounces semisweet chocolate, chopped and 1 teaspoon vanilla extract in a bowl.
In a small saucepan, heat ⅓ cup unsalted butter, ⅔ cup brown sugar and 2 tablespoons water. When it breaks to a boil, remove from the heat and immediately add it to the chocolate. Let stand for 30 seconds and stir well with a whisk until smooth. Let stand for 5 minutes before adding the rest of the ingredients.
Add 2 eggs at the same time and mix well.
Add the sifted ¾ cup all-purpose flour, ¼ teaspoon baking soda and ¼ teaspoon salt. You can sift them before or have the ingredients measured and sift them directly over the butter mixture (my choice).
Mix well until the batter is smooth and shiny, and spread evenly in the prepared pan.
Scatter ½ cup coarsely chopped walnuts on top and bake for about 20 minutes, until the top is dry but still jiggles in the center. It might be slightly cracked in parts. Don’t overbake them, or they will be dry.
Let cool completely on a wire rack.
Run a smooth-bladed knife around the edges to loosen up any bit that might be stuck, and lift the whole block with the help of the paper. Transfer to a flat surface and cut into squares.
Keep covered in plastic wrap or in an airtight container.