Preheat the oven to 325 degrees F. Butter an 8-inch square baking dish with 1 teaspoon butter. Cut a piece of parchment paper in a strip to line the bottom and 2 sides of the dish. Butter the paper with the remaining 1/2 teaspoon butter and set aside.
Place the unsweetened chocolate and 8 tablespoons butter in a medium heat-proof bowl that fits comfortably over a saucepan filled with 1 inch water. Place the double-boiler over medium heat and cook, stirring constantly with a silicone spatula, until the chocolate and butter are just barely melted. Remove the bowl from the heat and continue to stir for 1 minute to cool slightly. The mixture should be warm to the touch, not hot.
Using a hand-held mixer, beat the sugar, vanilla and salt into the chocolate mixture until smooth. Add the eggs and yolk all at once and beat until fully incorporated and smooth. Fold in the flour and semisweet chocolate chips with a silicone spatula until just barely combined; a few streaks are fine. Pour the mixture into the prepared pan and bake on the middle rack until just set and a toothpick inserted in the center comes out clean, about 30 minutes. Do not overbake. Allow to cool to room temperature before cutting into 16 small pieces.
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