Preheat the oven to 350°F. Line an 8-inch square baking pan with foil, bringing the foil up the sides of the pan.

Place the chocolate in a deep metal bowl. Set the bowl in a skillet of barely simmering water. Stir occasionally until the chocolate is melted and smooth. Remove from over the water and using a plastic spatula, mix in the oil. Let cool to lukewarm.

With an electric mixer, beat the eggs in a medium bowl until thick and foamy. Beat in the sugar ¼ cup at a time. Using a rubber spatula, stir in the chocolate mixture. Add the flour and salt and mix vigorously with the rubber spatula until the batter thickens, about 40 seconds. Mix in the vanilla and walnuts.

Transfer the batter to the prepared pan, smoothing to even. Bake until just firm to the touch and a tester inserted in the center comes out almost clean, about 25 minutes.

Cool completely in the pan on a rack. Using the foil as an aid, remove the brownie from the pan. Cut into 12 or 16 pieces. (Can be made ahead. Cover and let stand at room temperature for up to 3 days, or wrap airtight and freeze.)